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Simplifying (x + 2)(x + -7) = (2x + 7)(x + -7) Reorder the terms: (2 + x)(x + -7) = (2x + 7)(x + -7) Reorder the terms: (2 + x)(-7 + x) = (2x + 7)(x + -7) Multiply (2 + x) * (-7 + x) (2(-7 + x) + x(-7 + x)) = (2x + 7)(x + -7) ((-7 * 2 + x * 2) + x(-7 + x)) = (2x + 7)(x + -7) ((-14 + 2x) + x(-7 + x)) = (2x + 7)(x + -7) (-14 + 2x + (-7 * x + x * x)) = (2x + 7)(x + -7) (-14 + 2x + (-7x + x2)) = (2x + 7)(x + -7) Combine like terms: 2x + -7x = -5x (-14 + -5x + x2) = (2x + 7)(x + -7) Reorder the terms: -14 + -5x + x2 = (7 + 2x)(x + -7) Reorder the terms: -14 + -5x + x2 = (7 + 2x)(-7 + x) Multiply (7 + 2x) * (-7 + x) -14 + -5x + x2 = (7(-7 + x) + 2x * (-7 + x)) -14 + -5x + x2 = ((-7 * 7 + x * 7) + 2x * (-7 + x)) -14 + -5x + x2 = ((-49 + 7x) + 2x * (-7 + x)) -14 + -5x + x2 = (-49 + 7x + (-7 * 2x + x * 2x)) -14 + -5x + x2 = (-49 + 7x + (-14x + 2x2)) Combine like terms: 7x + -14x = -7x -14 + -5x + x2 = (-49 + -7x + 2x2) Solving -14 + -5x + x2 = -49 + -7x + 2x2 Solving for variable 'x'. Reorder the terms: -14 + 49 + -5x + 7x + x2 + -2x2 = -49 + -7x + 2x2 + 49 + 7x + -2x2 Combine like terms: -14 + 49 = 35 35 + -5x + 7x + x2 + -2x2 = -49 + -7x + 2x2 + 49 + 7x + -2x2 Combine like terms: -5x + 7x = 2x 35 + 2x + x2 + -2x2 = -49 + -7x + 2x2 + 49 + 7x + -2x2 Combine like terms: x2 + -2x2 = -1x2 35 + 2x + -1x2 = -49 + -7x + 2x2 + 49 + 7x + -2x2 Reorder the terms: 35 + 2x + -1x2 = -49 + 49 + -7x + 7x + 2x2 + -2x2 Combine like terms: -49 + 49 = 0 35 + 2x + -1x2 = 0 + -7x + 7x + 2x2 + -2x2 35 + 2x + -1x2 = -7x + 7x + 2x2 + -2x2 Combine like terms: -7x + 7x = 0 35 + 2x + -1x2 = 0 + 2x2 + -2x2 35 + 2x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 35 + 2x + -1x2 = 0 Factor a trinomial. (7 + -1x)(5 + x) = 0Subproblem 1
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 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 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. 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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