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Simplifying 27x + -50 = x2 + 47x + 50 Reorder the terms: -50 + 27x = x2 + 47x + 50 Reorder the terms: -50 + 27x = 50 + 47x + x2 Solving -50 + 27x = 50 + 47x + x2 Solving for variable 'x'. Reorder the terms: -50 + -50 + 27x + -47x + -1x2 = 50 + 47x + x2 + -50 + -47x + -1x2 Combine like terms: -50 + -50 = -100 -100 + 27x + -47x + -1x2 = 50 + 47x + x2 + -50 + -47x + -1x2 Combine like terms: 27x + -47x = -20x -100 + -20x + -1x2 = 50 + 47x + x2 + -50 + -47x + -1x2 Reorder the terms: -100 + -20x + -1x2 = 50 + -50 + 47x + -47x + x2 + -1x2 Combine like terms: 50 + -50 = 0 -100 + -20x + -1x2 = 0 + 47x + -47x + x2 + -1x2 -100 + -20x + -1x2 = 47x + -47x + x2 + -1x2 Combine like terms: 47x + -47x = 0 -100 + -20x + -1x2 = 0 + x2 + -1x2 -100 + -20x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -100 + -20x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(100 + 20x + x2) = 0 Factor a trinomial. -1((10 + x)(10 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 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 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Simplifying x = -10Subproblem 2
Set the factor '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 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 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Simplifying x = -10Solution
x = {-10, -10}
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