Solving Quadratic Equations by Completing the Square
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
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| x^2+10x=56 Solve for x by completing the square. | Take half of the coefficient of the x-term (10/2=5) and then square that number to get 25. Now add 25 to both sides so you will get x^2+10x+25=81. Now you can factor the equation to (x+5)^2=81. Use the square root property to solve for x. x=4 and x=-14
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| x^2+12x=-56 Solve for x by completing the square. | Take half the coefficient of the x-term and square it to get 36. Add 36 to both sides then factor to get (x+6)^2=-20. Take the square root of each side and solve for x to get x=-6+or-2isquareroot5
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| x^2+2x=16 Solve for x by completing the square. | Take half of the coefficient of the x-term and then square that number to get 1. Add 1 to both sides of the equation and then factor to get (x+1)^2=17. Take square root of both sides to solve for x to get x=-1+or-squareroot17
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| Add the proper constant to the binomial so that the resulting trinomial is a perfect square. x^2+16x+___ | Take half of the coefficient of the x-term (16/2=8) and then square it to get 64.
x^2+16x+64
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| 4x^2+16x=24 Solve for x by completing the square. | First, divide both sides by 4. Then take half of the coefficient of the x-term (4/2=2) and then square it (4). Add 4 to both sides and then factor to (x+2)^2=10. Use the square root property and solve for x to get x=-2+or-squareroot10
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| Add the proper constant to the binomial so that the resulting trinomial is a perfect square. x^2-4x+____ | Take half of the coefficient of the x-term (-4/2=-2) and then square it to get 4.
x^2-4x+4
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| Add the proper constant to the binomial so that the resulting trinomial is a perfect square. x^2+32x+___ | Take half of the coefficient of the x-term (32/2=16) and then square it to get 256.
x^2+32x+256
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| (x+5)^2=25 Use the square root property to solve for x | Take the square root of both sides to get x+5=+or-5 and then subtract 5 to solve for x and get x=0 or x=-10
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| x^2-5=0 Use the square root property to solve for x | Subtract 5 from the left side to get x^2=5. Then use the square root property to get x=+or-squareroot of 5
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| x^2+5x-36=0 Solve for x by completing the square. | First move the 36 to the other side by adding 36 to 0. Take half of the coefficient of the x-term (5/2) and then square it to get (25/4). Add 25/4 to both sides and now factor and then use the square root property to solve for x. x=4 and x=-9
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