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Simplifying x(7x + 13) = 2x2 + -8x + 54 Reorder the terms: x(13 + 7x) = 2x2 + -8x + 54 (13 * x + 7x * x) = 2x2 + -8x + 54 (13x + 7x2) = 2x2 + -8x + 54 Reorder the terms: 13x + 7x2 = 54 + -8x + 2x2 Solving 13x + 7x2 = 54 + -8x + 2x2 Solving for variable 'x'. Reorder the terms: -54 + 13x + 8x + 7x2 + -2x2 = 54 + -8x + 2x2 + -54 + 8x + -2x2 Combine like terms: 13x + 8x = 21x -54 + 21x + 7x2 + -2x2 = 54 + -8x + 2x2 + -54 + 8x + -2x2 Combine like terms: 7x2 + -2x2 = 5x2 -54 + 21x + 5x2 = 54 + -8x + 2x2 + -54 + 8x + -2x2 Reorder the terms: -54 + 21x + 5x2 = 54 + -54 + -8x + 8x + 2x2 + -2x2 Combine like terms: 54 + -54 = 0 -54 + 21x + 5x2 = 0 + -8x + 8x + 2x2 + -2x2 -54 + 21x + 5x2 = -8x + 8x + 2x2 + -2x2 Combine like terms: -8x + 8x = 0 -54 + 21x + 5x2 = 0 + 2x2 + -2x2 -54 + 21x + 5x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -54 + 21x + 5x2 = 0 Factor a trinomial. (-6 + -1x)(9 + -5x) = 0Subproblem 1
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 = -6Subproblem 2
Set the factor '(9 + -5x)' equal to zero and attempt to solve: Simplifying 9 + -5x = 0 Solving 9 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -5x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -5x = 0 + -9 -5x = 0 + -9 Combine like terms: 0 + -9 = -9 -5x = -9 Divide each side by '-5'. x = 1.8 Simplifying x = 1.8Solution
x = {-6, 1.8}
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