Question

Solve the equation by completing the square. Show all solutions8x^2 + 16x = 42

Answer 1

8x² + 16x = 42​

x² + 16/8x = 42​/8 dividing by 8 at both sides

x² + 2x = 5.25

x² + 2x - 5.25 = 0

If we compute (x + 1)², we get:

(x + 1)² = x² + 2*x*1 + 1² = x² + 2x + 1

Then,

x² + 2x - 5.25 + 1 - 1 = 0

(x² + 2x + 1) + (-5.25 - 1) = 0

(x + 1)² - 6.25 = 0

(x + 1)² = 6.25

x + 1 = √6.25

This has 2 solutions,

x + 1 = 2.5 or x + 1 = -2.5

x = 2.5 - 1 x = -2.5 - 1

x = 1.5 x = -3.5