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Simplifying x(9x + 16) = 4x2 + -6x + 15 Reorder the terms: x(16 + 9x) = 4x2 + -6x + 15 (16 * x + 9x * x) = 4x2 + -6x + 15 (16x + 9x2) = 4x2 + -6x + 15 Reorder the terms: 16x + 9x2 = 15 + -6x + 4x2 Solving 16x + 9x2 = 15 + -6x + 4x2 Solving for variable 'x'. Reorder the terms: -15 + 16x + 6x + 9x2 + -4x2 = 15 + -6x + 4x2 + -15 + 6x + -4x2 Combine like terms: 16x + 6x = 22x -15 + 22x + 9x2 + -4x2 = 15 + -6x + 4x2 + -15 + 6x + -4x2 Combine like terms: 9x2 + -4x2 = 5x2 -15 + 22x + 5x2 = 15 + -6x + 4x2 + -15 + 6x + -4x2 Reorder the terms: -15 + 22x + 5x2 = 15 + -15 + -6x + 6x + 4x2 + -4x2 Combine like terms: 15 + -15 = 0 -15 + 22x + 5x2 = 0 + -6x + 6x + 4x2 + -4x2 -15 + 22x + 5x2 = -6x + 6x + 4x2 + -4x2 Combine like terms: -6x + 6x = 0 -15 + 22x + 5x2 = 0 + 4x2 + -4x2 -15 + 22x + 5x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -15 + 22x + 5x2 = 0 Factor a trinomial. (-5 + -1x)(3 + -5x) = 0Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 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 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 2
Set the factor '(3 + -5x)' equal to zero and attempt to solve: Simplifying 3 + -5x = 0 Solving 3 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5x = 0 + -3 -5x = 0 + -3 Combine like terms: 0 + -3 = -3 -5x = -3 Divide each side by '-5'. x = 0.6 Simplifying x = 0.6Solution
x = {-5, 0.6}
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