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Simplifying x(5x + 5) = 2x2 + -5x + 48 Reorder the terms: x(5 + 5x) = 2x2 + -5x + 48 (5 * x + 5x * x) = 2x2 + -5x + 48 (5x + 5x2) = 2x2 + -5x + 48 Reorder the terms: 5x + 5x2 = 48 + -5x + 2x2 Solving 5x + 5x2 = 48 + -5x + 2x2 Solving for variable 'x'. Reorder the terms: -48 + 5x + 5x + 5x2 + -2x2 = 48 + -5x + 2x2 + -48 + 5x + -2x2 Combine like terms: 5x + 5x = 10x -48 + 10x + 5x2 + -2x2 = 48 + -5x + 2x2 + -48 + 5x + -2x2 Combine like terms: 5x2 + -2x2 = 3x2 -48 + 10x + 3x2 = 48 + -5x + 2x2 + -48 + 5x + -2x2 Reorder the terms: -48 + 10x + 3x2 = 48 + -48 + -5x + 5x + 2x2 + -2x2 Combine like terms: 48 + -48 = 0 -48 + 10x + 3x2 = 0 + -5x + 5x + 2x2 + -2x2 -48 + 10x + 3x2 = -5x + 5x + 2x2 + -2x2 Combine like terms: -5x + 5x = 0 -48 + 10x + 3x2 = 0 + 2x2 + -2x2 -48 + 10x + 3x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -48 + 10x + 3x2 = 0 Factor a trinomial. (-6 + -1x)(8 + -3x) = 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 '(8 + -3x)' equal to zero and attempt to solve: Simplifying 8 + -3x = 0 Solving 8 + -3x = 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 + -3x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3x = 0 + -8 -3x = 0 + -8 Combine like terms: 0 + -8 = -8 -3x = -8 Divide each side by '-3'. x = 2.666666667 Simplifying x = 2.666666667Solution
x = {-6, 2.666666667}
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