Which is a solution to (x - 2)(x + 10) = 13?
x = 3, x = 8, x = 10, x = 11

Solution:

Let us first simplify the equation, then factorize using the method splitting the middle term.

Step 1: Given, (x - 2)(x + 10) = 13

x² + 10x - 2x - 20 = 13

x² + 8x - 20 = 13

Subtract 13 from both sides.

x² + 8x - 33 = 0

Step 2: Factorize the quadratic equation by splitting the middle term.

Since, 33 can be factored into 11 and 3 to sum up 8

x² + 11x - 3x - 33 = 0

x(x + 11) - 3(x + 11) = 0

(x - 3)(x + 11) = 0

Step 3: Put both the factors equal to zero.

(x - 3) = 0 and (x + 11) = 0

x = 3 and x = -11

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Which is a solution to (x - 2)(x + 10) = 13?

Summary:

The solution to the equation (x - 2)(x + 10) = 13 which satisfies the equation is x = 3 and x = -11.