Page 715 - Algebra 1

Example
3
700 Saxon Algebra 1
Solving ax2 + bx = c by Completing the Square Solve by completing the square.
a. 4x2+16x=8 SOLUTION
Write the equation so that the coefficient of x2 is 1. Then complete the square.
2 Divide both sides by the coefficient of x .
Simplify.
Complete the square. Add the missing value to both sides of the equation.
Simplify the fraction. Simplify.
Factor the left side. Simplify the right side.
Take the square root of both sides. Simplify.
Write as two equations. Subtraction Property of Equality Simplify.
Use a calculator to find approximate values.
Substitute -4.450 for x. Square (-4.450). Multiply.
Subtract.
Substitute 0.450 for x. Square (0.450). Multiply.
Subtract.
_2
4x +16x=8
4x2 + 16x = 8 _
44 x2 +4x=2
_4 2
x2 +4x+(2)=2+(2)
x2 +4x+(2)2 =2+(2)2 x2 +4x+4=2+4
(x+2)2 =6 √
√(x+2)2=± 6 x + 2 = ± √ 6
x+2=-√6 or x+2=√6 -_ _ 2 = -_ _ 2 _ - _ 2 = -_ _ 2
x=-2-√6 or x=-2+√6 x ≈ -4.450 or x ≈ 0.450
Check
4x2 +16x=8 2 Q
4(-4.450) + 16(-4.450) ≈ 8 Q
4(19.8025) + 16(-4.450) ≈ 8 Q
79.21 - 71.2 ≈ 8 8.01 ≈ 8 4x2 +16x=8
✓
✓
2 Q 4(0.450) + 16(0.450) ≈ 8
Q 4(0.2025) + 16(0.450) ≈ 8
Q 0.81 + 7.2 ≈ 8
8.01 ≈ 8
_4 2