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Simplifying 2x2 + -2x = 32 Reorder the terms: -2x + 2x2 = 32 Solving -2x + 2x2 = 32 Solving for variable 'x'. Reorder the terms: -32 + -2x + 2x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + -2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + -1x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-16 + -1x + x2)' equal to zero and attempt to solve: Simplifying -16 + -1x + x2 = 0 Solving -16 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -1x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + -1x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -1x + x2 = 0 + 16 -1x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -1x + x2 = 16 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 = 16 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 16 + 0.25 Combine like terms: 16 + 0.25 = 16.25 0.25 + -1x + x2 = 16.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (x + -0.5) equal to 4.031128874 and -4.031128874.Subproblem 1
x + -0.5 = 4.031128874 Simplifying x + -0.5 = 4.031128874 Reorder the terms: -0.5 + x = 4.031128874 Solving -0.5 + x = 4.031128874 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 = 4.031128874 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 4.031128874 + 0.5 x = 4.031128874 + 0.5 Combine like terms: 4.031128874 + 0.5 = 4.531128874 x = 4.531128874 Simplifying x = 4.531128874Subproblem 2
x + -0.5 = -4.031128874 Simplifying x + -0.5 = -4.031128874 Reorder the terms: -0.5 + x = -4.031128874 Solving -0.5 + x = -4.031128874 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 = -4.031128874 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -4.031128874 + 0.5 x = -4.031128874 + 0.5 Combine like terms: -4.031128874 + 0.5 = -3.531128874 x = -3.531128874 Simplifying x = -3.531128874Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.531128874, -3.531128874}Solution
x = {4.531128874, -3.531128874}
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