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Simplifying x2 + -11x + -12 = -1x2 + 39x + -108 Reorder the terms: -12 + -11x + x2 = -1x2 + 39x + -108 Reorder the terms: -12 + -11x + x2 = -108 + 39x + -1x2 Solving -12 + -11x + x2 = -108 + 39x + -1x2 Solving for variable 'x'. Reorder the terms: -12 + 108 + -11x + -39x + x2 + x2 = -108 + 39x + -1x2 + 108 + -39x + x2 Combine like terms: -12 + 108 = 96 96 + -11x + -39x + x2 + x2 = -108 + 39x + -1x2 + 108 + -39x + x2 Combine like terms: -11x + -39x = -50x 96 + -50x + x2 + x2 = -108 + 39x + -1x2 + 108 + -39x + x2 Combine like terms: x2 + x2 = 2x2 96 + -50x + 2x2 = -108 + 39x + -1x2 + 108 + -39x + x2 Reorder the terms: 96 + -50x + 2x2 = -108 + 108 + 39x + -39x + -1x2 + x2 Combine like terms: -108 + 108 = 0 96 + -50x + 2x2 = 0 + 39x + -39x + -1x2 + x2 96 + -50x + 2x2 = 39x + -39x + -1x2 + x2 Combine like terms: 39x + -39x = 0 96 + -50x + 2x2 = 0 + -1x2 + x2 96 + -50x + 2x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 96 + -50x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(48 + -25x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(48 + -25x + x2)' equal to zero and attempt to solve: Simplifying 48 + -25x + x2 = 0 Solving 48 + -25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-48' to each side of the equation. 48 + -25x + -48 + x2 = 0 + -48 Reorder the terms: 48 + -48 + -25x + x2 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + -25x + x2 = 0 + -48 -25x + x2 = 0 + -48 Combine like terms: 0 + -48 = -48 -25x + x2 = -48 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = -48 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -48 + 156.25 Combine like terms: -48 + 156.25 = 108.25 156.25 + -25x + x2 = 108.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 108.25 Calculate the square root of the right side: 10.404326023 Break this problem into two subproblems by setting (x + -12.5) equal to 10.404326023 and -10.404326023.Subproblem 1
x + -12.5 = 10.404326023 Simplifying x + -12.5 = 10.404326023 Reorder the terms: -12.5 + x = 10.404326023 Solving -12.5 + x = 10.404326023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 10.404326023 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 10.404326023 + 12.5 x = 10.404326023 + 12.5 Combine like terms: 10.404326023 + 12.5 = 22.904326023 x = 22.904326023 Simplifying x = 22.904326023Subproblem 2
x + -12.5 = -10.404326023 Simplifying x + -12.5 = -10.404326023 Reorder the terms: -12.5 + x = -10.404326023 Solving -12.5 + x = -10.404326023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -10.404326023 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -10.404326023 + 12.5 x = -10.404326023 + 12.5 Combine like terms: -10.404326023 + 12.5 = 2.095673977 x = 2.095673977 Simplifying x = 2.095673977Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.904326023, 2.095673977}Solution
x = {22.904326023, 2.095673977}
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