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Simplifying x(9x + 28) = 4x2 + -9x + 24 Reorder the terms: x(28 + 9x) = 4x2 + -9x + 24 (28 * x + 9x * x) = 4x2 + -9x + 24 (28x + 9x2) = 4x2 + -9x + 24 Reorder the terms: 28x + 9x2 = 24 + -9x + 4x2 Solving 28x + 9x2 = 24 + -9x + 4x2 Solving for variable 'x'. Reorder the terms: -24 + 28x + 9x + 9x2 + -4x2 = 24 + -9x + 4x2 + -24 + 9x + -4x2 Combine like terms: 28x + 9x = 37x -24 + 37x + 9x2 + -4x2 = 24 + -9x + 4x2 + -24 + 9x + -4x2 Combine like terms: 9x2 + -4x2 = 5x2 -24 + 37x + 5x2 = 24 + -9x + 4x2 + -24 + 9x + -4x2 Reorder the terms: -24 + 37x + 5x2 = 24 + -24 + -9x + 9x + 4x2 + -4x2 Combine like terms: 24 + -24 = 0 -24 + 37x + 5x2 = 0 + -9x + 9x + 4x2 + -4x2 -24 + 37x + 5x2 = -9x + 9x + 4x2 + -4x2 Combine like terms: -9x + 9x = 0 -24 + 37x + 5x2 = 0 + 4x2 + -4x2 -24 + 37x + 5x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -24 + 37x + 5x2 = 0 Factor a trinomial. (-8 + -1x)(3 + -5x) = 0Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve: Simplifying -8 + -1x = 0 Solving -8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1x = 0 + 8 -1x = 0 + 8 Combine like terms: 0 + 8 = 8 -1x = 8 Divide each side by '-1'. x = -8 Simplifying x = -8Subproblem 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 = {-8, 0.6}
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