(x - 2)(x + 10) = 13
Expanding the equation:
x^2 + 10x - 2x - 20 = 13
Combine like terms:
x^2 + 8x - 20 = 13
Now, subtract 13 from both sides:
x^2 + 8x - 20 - 13 = 0
Simplify:
x^2 + 8x - 33 = 0
Now, you can use the quadratic formula to find the solutions for x:
x = (-b ± √(b² - 4ac)) / (2a)
In this equation, a = 1, b = 8, and c = -33. Plugging these values into the formula:
x = (-8 ± √(8² - 4 * 1 * (-33))) / (2 * 1)
x = (-8 ± √(64 + 132)) / 2
x = (-8 ± √196) / 2
x = (-8 ± 14) / 2
Now, you have two potential solutions:
1. x = (-8 + 14) / 2 = 6 / 2 = 3
2. x = (-8 - 14) / 2 = -22 / 2 = -11
So, the solutions to the equation are x = 3 and x = -11.