Question

Another question I need help with:

Solve the equation. Round the solutions to the nearest hundredth. 4(x+5)²=32

Answer 1

4(x+5)^2=32 original equation
(x+5)^2=8 divide both sides by 4
x+5=2.83 take sqrt of both sides
x=-2.17 subtract both sides by 5, x=-2.17

Answer 2

4(x + 5)² = 32
4(x + 5)(x + 5) = 32
4(x(x + 5) + 5(x + 5)) = 32
4(x(x) + x(5) + 5(x) + 5(5)) = 32
4(x² + 5x + 5x + 25) = 32
4(x² + 10x + 25) = 32
4(x²) + 4(10x) + 4(25) = 32
4x² + 40x + 100 = 32
- 32 - 32
4x² + 40x + 68 = 0
x = -(40) ± √((40)² - 4(4)(68))
2(1)
x = -40 ± √(1600 - 1088)
2
x = -40 ± √(512)
2
x = -40 ± 16√(2)
2
x = -20 ± 8√(2)
x = -20 + 8√(2) U x = -20 - 8√(2)