Completing the Square to Find Complex Roots
Read this topicExplanations 14
- Completing the Square: How to find ccc ccc is the number you need to add to allow for factoring into a square polynomial. Follow these simple steps and you can find the value yo…
By Tommy San Miguel, Joshua Pan
- Sometimes you might see an quadratic equation which would be very hard to factor and the quadratic formula would be a lot of work. That's when it's time to use Completing The Sq…
By Vivian Loh, Ben Ferrara, Alex Federspiel
- If you ever want to solve a quadratic equation that might be hard to factor and very difficult to use Quadratic Formula on, it's time to use Completing the Square. Let's first s…
By Vivian Loh, Moor Xu, Eunji Kwon, Victor Wang
- Let's say we have a quadratic expression x2+4xx^2+4xx2+4x. We can model this with the diagram below: We can rearrange this to look like a square: We are able now to "complete th…
By Ben Ferrara, Eunji Kwon
- (Videos) Complete the Square by HEGARTYMATHS Here are two videos by HEGARTYMATHS explaining how you set up a problem involving completing the square and secondly, how you solve …
By Alex Federspiel
- (Videos) Completing the Square by PatrickJMT Here's a video by PatrickJMT showing you how to complete the square. Patrick JMT has a good video explaining how to complete the squ…
By Ben Ferrara, Alex Federspiel, Eunji Kwon, Joshua Siktar
- (Videos) Completing the Square to Solve Quadratics by PatrickJMT Patrick JMT has a bunch of videos with examples for completing the square if you need more practice. In this fir…
By Ben Ferrara, Alex Federspiel, Jonathan Heller, Joshua Siktar
- (Video) Solve by Completing the Square by HEGARTYMATHS Here's another video by HEGARTYMATHS on completing the square. In this video he goes through some examples where your answ…
By Alex Federspiel, Eunji Kwon
- (Videos) Complete the Square by HEGARTYMATHS Here's two more videos by HEGARTYMATHS on completing the square. He goes over how you do it and how to solve for xxx. There are a lo…
By Alex Federspiel, Eunji Kwon
- (Video) How to Solve by Completing the Square by Brian McLogan In this video by Brian McLogan it is shown how to complete the square. The first example he looks at is: x2+4x=10x…
By Stefan Cuevas, Alex Federspiel, Eunji Kwon, Joshua Siktar
- (Video) Completing the Square by yaymath Here's a video by yaymath showing you how to find ccc when completing the square and then how to factor the new quadratic and solve. Som…
By Alex Federspiel
- (Videos) Completing the Square by mathman1024 Here's a video by mathman1024 showing you how to complete the square. The goal of completing the square is to find the missing piec…
By Alex Federspiel, Victor Wang
- Completing the Square: the Basics Back when we were working with quadratics, we learned how to use completing the square to find the vector form of a quadratic. We'll do a reall…
By Anusha Rahman
- (Video) Completing the Square with Complex Roots by Krista King In this video by Krista King, you will see an example of using the complete the square method to find complex roo…
By Anusha Rahman
Problems 48
- Solve for x. 0.25x2−0.4x−25=170.25x^2-0.4x-25=170.25x2−0.4x−25=17
- Find the solutions of x2−2x=15x^2 - 2x = 15x2−2x=15.
- Solve the quadratic equation x(x+8)=−16x(x+8)=-16x(x+8)=−16. Mark all solutions xxx below.
- What constant ccc would you add to both sides of the equation 0=x2−30x0=x^2-30x0=x2−30x to complete the square?
- What constant ccc would you add to both sides of the equation 0=x2−x0=x^2-x0=x2−x to complete the square?
- Complete the square to find the root(s) of the quadratic function y(x)=x2+18x−12y(x) = x^2+18x-12y(x)=x2+18x−12, rounded to the nearest hundredth.
- Complete the square to find the root(s) of 0=x2−10x+30=x^2-10x+30=x2−10x+3, rounded to the nearest hundredth.
- True or False\text{True or False}True or False === Given an equation of the form x2+bx=5x^2 + bx = 5x2+bx=5, you would complete the square by adding c=b24c=\frac{b^2}{4}c=4b2 t…
- Complete the square to find the solutions of 0=3x2−42x+420=3x^2-42x+420=3x2−42x+42, rounded to the nearest hundredth.
- Suppose a quadratic y=ax2+bx+cy = ax^2+bx+cy=ax2+bx+c has vertex at (k,k)(k,k)(k,k) and yyy-intercept at (0,2k)(0,2k)(0,2k) for some k≠0k\ne0k=0. Find bbb.
- Solve for x. 5=x2+4x5=x^2+4x5=x2+4x
- Solve for x. 0=(x2)+12x0=(x^2)+12x0=(x2)+12x
- Solve for x. 2x2−8x=102x^2-8x=102x2−8x=10
- Solve for x. 4x2+4x=124x^2+4x=124x2+4x=12
- Solve for x. 8x2+8x+8=08x^2+8x+8=08x2+8x+8=0
- Solve for x. 13x2+26x−36=1313x^2+26x-36=1313x2+26x−36=13
- Solve for x. 5x2−50x−15=255x^2-50x-15=255x2−50x−15=25
- Solve for xxx. Round to the nearest ten-thousandth. 7x2−4.5x=167x^2-4.5x=167x2−4.5x=16
- Solve for x. 18 x2+12 x=14\frac18\ x^2+\frac12\ x=\frac1481 x2+21 x=41
- For some value of ccc, the equation x2−4x+c=0x^2 - 4x + c = 0x2−4x+c=0 has exactly one solution. What is this solution?
- For fixed c>0c > 0c>0, how many values of bbb make the equation x2+bx+c=0x^2 + bx + c = 0x2+bx+c=0 have exactly one solution?
- Fix n∈Rn \in \mathbb{R}n∈R such that x2+(n−2)x−2n=0x^2 + (n-2)x - 2n = 0x2+(n−2)x−2n=0 has exactly one solution. What is nnn?
- The equation x2+10x+c=0x^2 + 10x + c = 0x2+10x+c=0 has exactly one solution. Find ccc.
- The equation 2x2−16x+c=02x^2 - 16x + c= 02x2−16x+c=0 has exactly one solution. Find ccc.
- How many real solutions xxx does the equation x2+20x=−99x^2 + 20x = -99x2+20x=−99 have?
- How many real solutions xxx are there to the equation x2+20x=−100x^2 + 20x = -100x2+20x=−100?
- Does x2−4x=−πx^2 - 4x = -\pix2−4x=−π have real solutions xxx? If so, find their sum.
- Find the number of real solutions xxx to the equation x2+20x=−101x^2 + 20x = -101x2+20x=−101.
- The equation πx2−π2x=π2x+3π3\pi x^2 - \pi^2 x = \pi^2 x + 3\pi^3πx2−π2x=π2x+3π3 has two distinct real solutions, x=rx=rx=r and x=sx=sx=s, with r<sr<sr<s. Find their difference, …
- Mark all solutions xxx below to the equation πx2−π2x=π2x\pi x^2 - \pi^2 x = \pi^2 xπx2−π2x=π2x.
- Given x2+2xy=25−y2x^2 + 2xy = 25-y^2x2+2xy=25−y2, solve for yyy in terms of xxx.
- Her competitor, Paper Jones, knows the equation satisfied by aaa and bbb, but not the exact dimensions. What can Jones say for sure about aaa and bbb?
- Select every equation below in which one side is a perfect square quadratic (in any form), while the other side is a constant.
- Select every equation below in which one side is a perfect square quadratic (in any form), while the other side is a constant.
- Who is right?
- Solve 3x2−12x+3=303x^2-12x+3 = 303x2−12x+3=30 for xxx.
- ax2+bx=kax^2 + bx = kax2+bx=k Say you were to solve for xxx. After dividing both sides by aaa, what value would you need to add to each side of the equation to make a perfect sq…
- Solve for xxx: x2+2x=3x^2 +2x = 3x2+2x=3
- Solve for xxx: x2−4x=−3x^2 -4x = -3x2−4x=−3
- Solve for xxx: x2−9x=−20x^2 -9x = -20x2−9x=−20
- Solve for xxx: 6x2−18x=−126x^2 -18x = -126x2−18x=−12
- First, she divides both sides by 121212. What value would she then need to add to each side of the equation to make a perfect square?
- Solve for xxx: 12x2−10x=−212x^2 -10x = -212x2−10x=−2
- If you were trying to solve for xxx by completing the square, what value would you add to each side of the equation? x2−8x=−15x^2 -8x = -15x2−8x=−15
- Solve −x2−2x=1-x^2-2x = 1−x2−2x=1.
- Solve for xxx: x2+x=6x^2 +x = 6x2+x=6
- Find all values of xxx so that x2+7x=−12x^2+7x=-12x2+7x=−12. Check all that apply.
- What is the radius of the sphere that has equation x2−6x+y2+10y+z2+22z+119=0?x^2 - 6x + y^2 + 10y + z^2 + 22z + 119 = 0?x2−6x+y2+10y+z2+22z+119=0?