Question

(x-7)(x+3)+(x-1)(x+5)=102

Answer 1

Х²+3-7х-21+х²+5х-х-5=102
2х²+0-26=102
2х²-26=102
2х²=26+102
2х²=128
х²=64
х=±8

Answer 2

Let's solve the given equation step by step:

1. Expand the products on both sides of the equation: (x - 7)(x + 3) + (x - 1)(x + 5) = 102

   Expand the first product: x^2 + 3x - 7x - 21 Expand the second product: x^2 + 5x - 1x - 5

2. Combine like terms: x^2 + 3x - 7x - 21 + x^2 + 5x - 1x - 5 = 102

   Simplify the terms: 2x^2 + 0x - 26 = 102

3. Move the constant term to the other side of the equation: 2x^2 - 26 = 102

4. Add 26 to both sides of the equation: 2x^2 = 128

5. Divide both sides by 2: x^2 = 64

6. Take the square root of both sides: x = ±8

So, the solutions for the equation are x = 8 and x = -8.