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Simplifying (5x + -5)(x + -5) = (2x + -11)(2x + 5) Reorder the terms: (-5 + 5x)(x + -5) = (2x + -11)(2x + 5) Reorder the terms: (-5 + 5x)(-5 + x) = (2x + -11)(2x + 5) Multiply (-5 + 5x) * (-5 + x) (-5(-5 + x) + 5x * (-5 + x)) = (2x + -11)(2x + 5) ((-5 * -5 + x * -5) + 5x * (-5 + x)) = (2x + -11)(2x + 5) ((25 + -5x) + 5x * (-5 + x)) = (2x + -11)(2x + 5) (25 + -5x + (-5 * 5x + x * 5x)) = (2x + -11)(2x + 5) (25 + -5x + (-25x + 5x2)) = (2x + -11)(2x + 5) Combine like terms: -5x + -25x = -30x (25 + -30x + 5x2) = (2x + -11)(2x + 5) Reorder the terms: 25 + -30x + 5x2 = (-11 + 2x)(2x + 5) Reorder the terms: 25 + -30x + 5x2 = (-11 + 2x)(5 + 2x) Multiply (-11 + 2x) * (5 + 2x) 25 + -30x + 5x2 = (-11(5 + 2x) + 2x * (5 + 2x)) 25 + -30x + 5x2 = ((5 * -11 + 2x * -11) + 2x * (5 + 2x)) 25 + -30x + 5x2 = ((-55 + -22x) + 2x * (5 + 2x)) 25 + -30x + 5x2 = (-55 + -22x + (5 * 2x + 2x * 2x)) 25 + -30x + 5x2 = (-55 + -22x + (10x + 4x2)) Combine like terms: -22x + 10x = -12x 25 + -30x + 5x2 = (-55 + -12x + 4x2) Solving 25 + -30x + 5x2 = -55 + -12x + 4x2 Solving for variable 'x'. Reorder the terms: 25 + 55 + -30x + 12x + 5x2 + -4x2 = -55 + -12x + 4x2 + 55 + 12x + -4x2 Combine like terms: 25 + 55 = 80 80 + -30x + 12x + 5x2 + -4x2 = -55 + -12x + 4x2 + 55 + 12x + -4x2 Combine like terms: -30x + 12x = -18x 80 + -18x + 5x2 + -4x2 = -55 + -12x + 4x2 + 55 + 12x + -4x2 Combine like terms: 5x2 + -4x2 = 1x2 80 + -18x + 1x2 = -55 + -12x + 4x2 + 55 + 12x + -4x2 Reorder the terms: 80 + -18x + 1x2 = -55 + 55 + -12x + 12x + 4x2 + -4x2 Combine like terms: -55 + 55 = 0 80 + -18x + 1x2 = 0 + -12x + 12x + 4x2 + -4x2 80 + -18x + 1x2 = -12x + 12x + 4x2 + -4x2 Combine like terms: -12x + 12x = 0 80 + -18x + 1x2 = 0 + 4x2 + -4x2 80 + -18x + 1x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 80 + -18x + 1x2 = 0 Factor a trinomial. (8 + -1x)(10 + -1x) = 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 '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Solution
x = {8, 10}
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