Question

Find the solutions to the equation 102x + 11 = (x + 6)2 – 2. Which values are approximate solutions to the equation? Check all that apply.

a.–9.6

b.–7.4

c.–4.6

d.–2.4

e.0.6

Answer 1

A. –9.6

D.–2.4

Explanation:

Answer 2

x = 0.256286, 89.7437

Explanation:

Step 1: Write equation

102x + 11 = (x + 6)² - 2

Step 2: Solve for x

1. Expand: 102x + 11 = x² + 12x + 36 - 2
2. Combine like terms: 102x + 11 = x² + 12x + 34
3. Subtract 11 on both sides: 102x = x² + 12x + 23
4. Subtract 102x on both sides: 0 = x² - 90x + 23
5. Quadratic Formula:
   `x=(90 \pm √((-90)^2-4(1)(23)) )/(2(1))`
6. Simplify: x = 0.256286, 89.7437