Verified Answer :

Answer: X=3

Step-by-step explanation:

1. expand the equation

x^2 + 10x -2x -20 = 13

2. Collect like terms

x^2 + 8x - 20 = 13

3. Simplify

x^2 + 8x = 13 + 20

x^2 + 8x = 33

x^2 = 33 - 8x

4. Substitute answers for guess and check

3^2 = 33 - (8 x 3)

9 = 33 - 24

This equation is correct therefore x = 3

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The solution to the given algebraic expression (x - 2)(x + 10) = 13 is x = 3

What is an algebraic equation?

An algebraic equation is the combination of variables and their coefficients(usually numbers) with arithmetic operations. The main purpose of an algebraic expression is to determine the value(s) of the variable(s).

From the given information:

(x - 2)(x + 10) = 13

x² + 10x - 2x - 20 = 13

x² + 8x -20 -13

x² + 8x - 33 = 0 (quadratic equation)

Using the quadratic formula, the values of x are - 11 and 3. Since we are considering only the positive integer only, x = 3

Learn more about algebraic equations here:

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