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Simplifying 127 + -2x2 = x2 + 33x + 34 Reorder the terms: 127 + -2x2 = 34 + 33x + x2 Solving 127 + -2x2 = 34 + 33x + x2 Solving for variable 'x'. Reorder the terms: 127 + -34 + -33x + -2x2 + -1x2 = 34 + 33x + x2 + -34 + -33x + -1x2 Combine like terms: 127 + -34 = 93 93 + -33x + -2x2 + -1x2 = 34 + 33x + x2 + -34 + -33x + -1x2 Combine like terms: -2x2 + -1x2 = -3x2 93 + -33x + -3x2 = 34 + 33x + x2 + -34 + -33x + -1x2 Reorder the terms: 93 + -33x + -3x2 = 34 + -34 + 33x + -33x + x2 + -1x2 Combine like terms: 34 + -34 = 0 93 + -33x + -3x2 = 0 + 33x + -33x + x2 + -1x2 93 + -33x + -3x2 = 33x + -33x + x2 + -1x2 Combine like terms: 33x + -33x = 0 93 + -33x + -3x2 = 0 + x2 + -1x2 93 + -33x + -3x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 93 + -33x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(31 + -11x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(31 + -11x + -1x2)' equal to zero and attempt to solve: Simplifying 31 + -11x + -1x2 = 0 Solving 31 + -11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -31 + 11x + x2 = 0 Move the constant term to the right: Add '31' to each side of the equation. -31 + 11x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + 11x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 11x + x2 = 0 + 31 11x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 11x + x2 = 31 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 31 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 31 + 30.25 Combine like terms: 31 + 30.25 = 61.25 30.25 + 11x + x2 = 61.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 61.25 Calculate the square root of the right side: 7.826237921 Break this problem into two subproblems by setting (x + 5.5) equal to 7.826237921 and -7.826237921.Subproblem 1
x + 5.5 = 7.826237921 Simplifying x + 5.5 = 7.826237921 Reorder the terms: 5.5 + x = 7.826237921 Solving 5.5 + x = 7.826237921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 7.826237921 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 7.826237921 + -5.5 x = 7.826237921 + -5.5 Combine like terms: 7.826237921 + -5.5 = 2.326237921 x = 2.326237921 Simplifying x = 2.326237921Subproblem 2
x + 5.5 = -7.826237921 Simplifying x + 5.5 = -7.826237921 Reorder the terms: 5.5 + x = -7.826237921 Solving 5.5 + x = -7.826237921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -7.826237921 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -7.826237921 + -5.5 x = -7.826237921 + -5.5 Combine like terms: -7.826237921 + -5.5 = -13.326237921 x = -13.326237921 Simplifying x = -13.326237921Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.326237921, -13.326237921}Solution
x = {2.326237921, -13.326237921}
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