Page 57 - Math Course 3 (Book 1)

Solving Quadratic Equations

Method 2 Complete the square. MO. 2 - L3b
1 –12
Step 1 Find of –12 = –6 Quadratic Equations:
2
2
2
Step 2 Square the result (–6) = 36 Completing the Square
of Step 1.

2
Step 3 Add the result of x –12x + 36 Key Concept
2
Step 2 to x – 12x.
c = 36
Answer 2 2 Completing the Square
Notice that x – 12x + 36 = (x – 6)
To complete the square for a quadratic expression
2
of the form x + bx , you can follow the steps below.
Your Turn! Step 1 Find 1 of b, the coefficient of x.
2

Irrational Roots Step 2 Square the result of Step 1.
2
Solve x + 8x + 16 = 3 by taking the square root of Step 3 Add the result of Step 2 to x + bx,
2
each side. Round to the nearest tenth if necessary. the original expression.
A. {–4}
B. {–2.3, –5.7}
C. {2.3, 5.7}
D. Ø
Let’s Begin
Answer

Solve an Equation by Completing the Square

Example

2
Complete the Square Solve x – 18x + 5 = –12 by completing the square.
2
Find the value of c that makes x + 14x + c a perfect Isolate the x and x terms. Then complete the
2
square. square and solve.
2
A. 7 x – 18x + 5 = –12 Original equation
B. 14 x + 18x – 5 – 5 = –12 – 5 Subtract 5 from each
2
C. 156 side.
D. 49
2
x – 18x = –17 Simplify.
Answer
–18
x – 18x + 81 = –17 + 81 Since = 81, add
2
2
81 to each side.
2
2
(x – 9) = 64 Factor x –18x + 81
(x – 9) = ±8 Take the square root of
each side

x – 9 + 9 = ±8 + 9 Add 9 to each side.
49