Download Completing the Square Notes

Name______________________________________
Solving Quadratic Equations by Completing the Square
Steps:
ax2 + bx + c = 0
Given: 2x2 = -8x + 12
1. Collect variable terms on 1 side and constants
on the other side.
2x2 + 8x = 12
2. If needed, divide both sides by a to make the
2(x2 + 4x ____) = 12 ____
2
coefficient of the x term 1.
2(x2 + 4x + 4) = 12 + 4(2)
2
3. Complete the square by adding (b/2) to both
2(x2 + 4x + 4) = 20
sides of the equation.
2(x + 2)2 = 20
4. Factor the variable expression as a perfect square.
(x + 2)2 = 10
5. Take the square root of both sides of the equation.
x + 2 = ±√10
6. Solve for the values of the variable.
x = -2 ±√10
__________________________________________________________________________________________________
Solve : 1. x2 + 8 = 6x
2. 4x + x2 = 24
3. x2 – 4x = -1
4. 2x2 + 8x - 16= 0
5. 4x2 + 11 = 59
6. (x+10)2 = 6
Name______________________________________
Solving Quadratic Equations by Completing the Square
Steps:
ax2 + bx + c = 0
Given: 2x2 = -8x + 12
1. Collect variable terms on 1 side and constants
on the other side.
2x2 + 8x = 12
2
2. If needed, divide both sides by a to make the
2(x + 4x ____) = 12 ____
2
coefficient of the x term 1.
2(x2 + 4x + 4) = 12 + 4(2)
3. Complete the square by adding (b/2)2 to both
2(x2 + 4x + 4) = 20
sides of the equation.
2(x + 2)2 = 20
4. Factor the variable expression as a perfect square.
(x + 2)2 = 10
5. Take the square root of both sides of the equation.
x + 2 = ±√10
6. Solve for the values of the variable.
x = -2 ±√10
__________________________________________________________________________________________________
Solve : 1. x2 + 8 = 6x
2. 4x + x2 = 24
3. x2 – 4x = -1
4. 2x2 + 8x - 16= 0
5. 4x2 + 11 = 59
6. (x+10)2 = 6