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Simplifying x(x + 7) + 5(x + 7) = 0 Reorder the terms: x(7 + x) + 5(x + 7) = 0 (7 * x + x * x) + 5(x + 7) = 0 (7x + x2) + 5(x + 7) = 0 Reorder the terms: 7x + x2 + 5(7 + x) = 0 7x + x2 + (7 * 5 + x * 5) = 0 7x + x2 + (35 + 5x) = 0 Reorder the terms: 35 + 7x + 5x + x2 = 0 Combine like terms: 7x + 5x = 12x 35 + 12x + x2 = 0 Solving 35 + 12x + x2 = 0 Solving for variable 'x'. Factor a trinomial. (7 + x)(5 + x) = 0Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Solution
x = {-7, -5}
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