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Simplifying x(5x + 5) = 2x2 + -11x + 35 Reorder the terms: x(5 + 5x) = 2x2 + -11x + 35 (5 * x + 5x * x) = 2x2 + -11x + 35 (5x + 5x2) = 2x2 + -11x + 35 Reorder the terms: 5x + 5x2 = 35 + -11x + 2x2 Solving 5x + 5x2 = 35 + -11x + 2x2 Solving for variable 'x'. Reorder the terms: -35 + 5x + 11x + 5x2 + -2x2 = 35 + -11x + 2x2 + -35 + 11x + -2x2 Combine like terms: 5x + 11x = 16x -35 + 16x + 5x2 + -2x2 = 35 + -11x + 2x2 + -35 + 11x + -2x2 Combine like terms: 5x2 + -2x2 = 3x2 -35 + 16x + 3x2 = 35 + -11x + 2x2 + -35 + 11x + -2x2 Reorder the terms: -35 + 16x + 3x2 = 35 + -35 + -11x + 11x + 2x2 + -2x2 Combine like terms: 35 + -35 = 0 -35 + 16x + 3x2 = 0 + -11x + 11x + 2x2 + -2x2 -35 + 16x + 3x2 = -11x + 11x + 2x2 + -2x2 Combine like terms: -11x + 11x = 0 -35 + 16x + 3x2 = 0 + 2x2 + -2x2 -35 + 16x + 3x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -35 + 16x + 3x2 = 0 Factor a trinomial. (-7 + -1x)(5 + -3x) = 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 + -3x)' equal to zero and attempt to solve: Simplifying 5 + -3x = 0 Solving 5 + -3x = 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 + -3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x = 0 + -5 -3x = 0 + -5 Combine like terms: 0 + -5 = -5 -3x = -5 Divide each side by '-3'. x = 1.666666667 Simplifying x = 1.666666667Solution
x = {-7, 1.666666667}
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