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Simplifying x(9x + 17) = 4x2 + -12x + 42 Reorder the terms: x(17 + 9x) = 4x2 + -12x + 42 (17 * x + 9x * x) = 4x2 + -12x + 42 (17x + 9x2) = 4x2 + -12x + 42 Reorder the terms: 17x + 9x2 = 42 + -12x + 4x2 Solving 17x + 9x2 = 42 + -12x + 4x2 Solving for variable 'x'. Reorder the terms: -42 + 17x + 12x + 9x2 + -4x2 = 42 + -12x + 4x2 + -42 + 12x + -4x2 Combine like terms: 17x + 12x = 29x -42 + 29x + 9x2 + -4x2 = 42 + -12x + 4x2 + -42 + 12x + -4x2 Combine like terms: 9x2 + -4x2 = 5x2 -42 + 29x + 5x2 = 42 + -12x + 4x2 + -42 + 12x + -4x2 Reorder the terms: -42 + 29x + 5x2 = 42 + -42 + -12x + 12x + 4x2 + -4x2 Combine like terms: 42 + -42 = 0 -42 + 29x + 5x2 = 0 + -12x + 12x + 4x2 + -4x2 -42 + 29x + 5x2 = -12x + 12x + 4x2 + -4x2 Combine like terms: -12x + 12x = 0 -42 + 29x + 5x2 = 0 + 4x2 + -4x2 -42 + 29x + 5x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -42 + 29x + 5x2 = 0 Factor a trinomial. (-7 + -1x)(6 + -5x) = 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 + -5x)' equal to zero and attempt to solve: Simplifying 6 + -5x = 0 Solving 6 + -5x = 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 + -5x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5x = 0 + -6 -5x = 0 + -6 Combine like terms: 0 + -6 = -6 -5x = -6 Divide each side by '-5'. x = 1.2 Simplifying x = 1.2Solution
x = {-7, 1.2}
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