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

Answer:

x = 0.256286, 89.7437

Step-by-step 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: $x=\frac{90 \pm \sqrt{(-90)^2-4(1)(23)} }{2(1)}$
6. Simplify: x = 0.256286, 89.7437