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Simplifying (x + -8)(x + -10) = -19x + 122 Reorder the terms: (-8 + x)(x + -10) = -19x + 122 Reorder the terms: (-8 + x)(-10 + x) = -19x + 122 Multiply (-8 + x) * (-10 + x) (-8(-10 + x) + x(-10 + x)) = -19x + 122 ((-10 * -8 + x * -8) + x(-10 + x)) = -19x + 122 ((80 + -8x) + x(-10 + x)) = -19x + 122 (80 + -8x + (-10 * x + x * x)) = -19x + 122 (80 + -8x + (-10x + x2)) = -19x + 122 Combine like terms: -8x + -10x = -18x (80 + -18x + x2) = -19x + 122 Reorder the terms: 80 + -18x + x2 = 122 + -19x Solving 80 + -18x + x2 = 122 + -19x Solving for variable 'x'. Reorder the terms: 80 + -122 + -18x + 19x + x2 = 122 + -19x + -122 + 19x Combine like terms: 80 + -122 = -42 -42 + -18x + 19x + x2 = 122 + -19x + -122 + 19x Combine like terms: -18x + 19x = 1x -42 + 1x + x2 = 122 + -19x + -122 + 19x Reorder the terms: -42 + 1x + x2 = 122 + -122 + -19x + 19x Combine like terms: 122 + -122 = 0 -42 + 1x + x2 = 0 + -19x + 19x -42 + 1x + x2 = -19x + 19x Combine like terms: -19x + 19x = 0 -42 + 1x + x2 = 0 Factor a trinomial. (-7 + -1x)(6 + -1x) = 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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-7, 6}
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