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```9.4 – Solving Quadratic
Equations By Completing The
Square
Ex. 1 a. Solve x2 – 12x + 36 = 0.
Ex. 1 a. Solve x2 – 12x + 36 = 0.
x2 – 12x + 36 = 0
Ex. 1 a. Solve x2 – 12x + 36 = 0.
x2 – 12x + 36 = 0
(x
)(x
)=0
Ex. 1 a. Solve x2 – 12x + 36 = 0.
x2 – 12x + 36 = 0
(x – 6)(x – 6) = 0
Ex. 1 a. Solve x2 – 12x + 36 = 0.
x2 – 12x + 36 = 0
(x – 6)(x – 6) = 0
(x – 6)2 = 0
Ex. 1 a. Solve x2 – 12x + 36 = 0.
x2 – 12x + 36 = 0
(x – 6)(x – 6) = 0
√(x – 6)2 = √0
Ex. 1 a. Solve x2 – 12x + 36 = 0.
x2 – 12x + 36 = 0
(x – 6)(x – 6) = 0
√(x – 6)2 = √0
x–6=0
Ex. 1 a. Solve x2 – 12x + 36 = 0.
x2 – 12x + 36 = 0
(x – 6)(x – 6) = 0
√(x – 6)2 = √0
x–6=0
x=6
b. Solve x2 + 8x + 16 = 0.
b. Solve x2 + 8x + 16 = 0.
x2 + 8x + 16 = 0
(x + 4)(x + 4) = 0
√(x + 4)2 = √ 0
x+4=0
x = -4
b. Solve x2 + 8x + 16 = 0.
x2 + 8x + 16 = 0
(x + 4)(x + 4) = 0
(x + 4)2 = 0
x+4=0
x = -4
Ex. 2 a. Solve x2 + 10x + 21 = 0 by
completing the square.
b. Solve x2 + 8x + 16 = 0.
x2 + 8x + 16 = 0
(x + 4)(x + 4) = 0
(x + 4)2 = 0
x+4=0
x = -4
Ex. 2 a. Solve x2 + 10x + 21 = 0 by
completing the square.
x2 + 10x + 21 = 0
b. Solve x2 + 8x + 16 = 0.
x2 + 8x + 16 = 0
(x + 4)(x + 4) = 0
(x + 4)2 = 0
x+4=0
x = -4
Ex. 2 a. Solve x2 + 10x + 21 = 0 by
completing the square.
x2 + 10x + 21 = 0
Want x2 + 10x + 25
b. Solve x2 + 8x + 16 = 0.
x2 + 8x + 16 = 0
(x + 4)(x + 4) = 0
(x + 4)2 = 0
x+4=0
x = -4
Ex. 2 a. Solve x2 + 10x + 21 = 0 by
completing the square.
x2 + 10x + 21 = 0
+4 +4
x2 + 10x + 25 = 4
b. Solve x2 + 8x + 16 = 0.
x2 + 8x + 16 = 0
(x + 4)(x + 4) = 0
(x + 4)2 = 0
x+4=0
x = -4
Ex. 2 a. Solve x2 + 10x + 21 = 0 by
completing the square.
x2 + 10x + 21 = 0
+4 +4
x2 + 10x + 25 = 4
(x + 5)2 = 4
b. Solve x2 + 8x + 16 = 0.
x2 + 8x + 16 = 0
(x + 4)(x + 4) = 0
(x + 4)2 = 0
x+4=0
x = -4
Ex. 2 a. Solve x2 + 10x + 21 = 0 by
completing the square.
x2 + 10x + 21 = 0
+4 +4
x2 + 10x + 25 = 4
(x + 5)2 = 4
x + 5 = ±2
b. Solve x2 + 8x + 16 = 0.
x2 + 8x + 16 = 0
(x + 4)(x + 4) = 0
(x + 4)2 = 0
x+4=0
x = -4
Ex. 2 a. Solve x2 + 10x + 21 = 0 by
completing the square.
x2 + 10x + 21 = 0
+4 +4
x2 + 10x + 25 = 4
(x + 5)2 = 4
x + 5 = ±2
x+5=2
b. Solve x2 + 8x + 16 = 0.
x2 + 8x + 16 = 0
(x + 4)(x + 4) = 0
(x + 4)2 = 0
x+4=0
x = -4
Ex. 2 a. Solve x2 + 10x + 21 = 0 by
completing the square.
x2 + 10x + 21 = 0
+4 +4
x2 + 10x + 25 = 4
(x + 5)2 = 4
x + 5 = ±2
x+5=2
x + 5 = -2
b. Solve x2 + 8x + 16 = 0.
x2 + 8x + 16 = 0
(x + 4)(x + 4) = 0
(x + 4)2 = 0
x+4=0
x = -4
Ex. 2 a. Solve x2 + 10x + 21 = 0 by
completing the square.
x2 + 10x + 21 = 0
+4 +4
x2 + 10x + 25 = 4
(x + 5)2 = 4
x + 5 = ±2
x+5=2
x + 5 = -2
x = -3
b. Solve x2 + 8x + 16 = 0.
x2 + 8x + 16 = 0
(x + 4)(x + 4) = 0
(x + 4)2 = 0
x+4=0
x = -4
Ex. 2 a. Solve x2 + 10x + 21 = 0 by
completing the square.
x2 + 10x + 21 = 0
+4 +4
x2 + 10x + 25 = 4
(x + 5)2 = 4
x + 5 = ±2
x+5=2
x + 5 = -2
x = -3
x = -7
b. Solve x2 + 14x = 12 by completing
the square.
b. Solve x2 + 14x = 12 by completing
the square.
x2 + 14x = 12
Want x2 + 14x + 49
x2 + 14x + 49 = 61
(x + 7)2 = 61
x + 7 = ±√61
x = -7 ± √61
x ≈ 0.8 or x ≈ -14.8
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