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Simplifying 2x2 + -2x = 66 Reorder the terms: -2x + 2x2 = 66 Solving -2x + 2x2 = 66 Solving for variable 'x'. Reorder the terms: -66 + -2x + 2x2 = 66 + -66 Combine like terms: 66 + -66 = 0 -66 + -2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-33 + -1x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-33 + -1x + x2)' equal to zero and attempt to solve: Simplifying -33 + -1x + x2 = 0 Solving -33 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + -1x + 33 + x2 = 0 + 33 Reorder the terms: -33 + 33 + -1x + x2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + -1x + x2 = 0 + 33 -1x + x2 = 0 + 33 Combine like terms: 0 + 33 = 33 -1x + x2 = 33 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 33 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 33 + 0.25 Combine like terms: 33 + 0.25 = 33.25 0.25 + -1x + x2 = 33.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 33.25 Calculate the square root of the right side: 5.766281297 Break this problem into two subproblems by setting (x + -0.5) equal to 5.766281297 and -5.766281297.Subproblem 1
x + -0.5 = 5.766281297 Simplifying x + -0.5 = 5.766281297 Reorder the terms: -0.5 + x = 5.766281297 Solving -0.5 + x = 5.766281297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 5.766281297 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 5.766281297 + 0.5 x = 5.766281297 + 0.5 Combine like terms: 5.766281297 + 0.5 = 6.266281297 x = 6.266281297 Simplifying x = 6.266281297Subproblem 2
x + -0.5 = -5.766281297 Simplifying x + -0.5 = -5.766281297 Reorder the terms: -0.5 + x = -5.766281297 Solving -0.5 + x = -5.766281297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -5.766281297 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -5.766281297 + 0.5 x = -5.766281297 + 0.5 Combine like terms: -5.766281297 + 0.5 = -5.266281297 x = -5.266281297 Simplifying x = -5.266281297Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.266281297, -5.266281297}Solution
x = {6.266281297, -5.266281297}
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