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Simplifying (x + -5)(x + 6) + (x + -5)(2x + 5) = 0 Reorder the terms: (-5 + x)(x + 6) + (x + -5)(2x + 5) = 0 Reorder the terms: (-5 + x)(6 + x) + (x + -5)(2x + 5) = 0 Multiply (-5 + x) * (6 + x) (-5(6 + x) + x(6 + x)) + (x + -5)(2x + 5) = 0 ((6 * -5 + x * -5) + x(6 + x)) + (x + -5)(2x + 5) = 0 ((-30 + -5x) + x(6 + x)) + (x + -5)(2x + 5) = 0 (-30 + -5x + (6 * x + x * x)) + (x + -5)(2x + 5) = 0 (-30 + -5x + (6x + x2)) + (x + -5)(2x + 5) = 0 Combine like terms: -5x + 6x = 1x (-30 + 1x + x2) + (x + -5)(2x + 5) = 0 Reorder the terms: -30 + 1x + x2 + (-5 + x)(2x + 5) = 0 Reorder the terms: -30 + 1x + x2 + (-5 + x)(5 + 2x) = 0 Multiply (-5 + x) * (5 + 2x) -30 + 1x + x2 + (-5(5 + 2x) + x(5 + 2x)) = 0 -30 + 1x + x2 + ((5 * -5 + 2x * -5) + x(5 + 2x)) = 0 -30 + 1x + x2 + ((-25 + -10x) + x(5 + 2x)) = 0 -30 + 1x + x2 + (-25 + -10x + (5 * x + 2x * x)) = 0 -30 + 1x + x2 + (-25 + -10x + (5x + 2x2)) = 0 Combine like terms: -10x + 5x = -5x -30 + 1x + x2 + (-25 + -5x + 2x2) = 0 Reorder the terms: -30 + -25 + 1x + -5x + x2 + 2x2 = 0 Combine like terms: -30 + -25 = -55 -55 + 1x + -5x + x2 + 2x2 = 0 Combine like terms: 1x + -5x = -4x -55 + -4x + x2 + 2x2 = 0 Combine like terms: x2 + 2x2 = 3x2 -55 + -4x + 3x2 = 0 Solving -55 + -4x + 3x2 = 0 Solving for variable 'x'. Factor a trinomial. (-11 + -3x)(5 + -1x) = 0Subproblem 1
Set the factor '(-11 + -3x)' equal to zero and attempt to solve: Simplifying -11 + -3x = 0 Solving -11 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -3x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -3x = 0 + 11 -3x = 0 + 11 Combine like terms: 0 + 11 = 11 -3x = 11 Divide each side by '-3'. x = -3.666666667 Simplifying x = -3.666666667Subproblem 2
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 = 5Solution
x = {-3.666666667, 5}
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