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Simplifying 2x2 + 6 = 32x Reorder the terms: 6 + 2x2 = 32x Solving 6 + 2x2 = 32x Solving for variable 'x'. Reorder the terms: 6 + -32x + 2x2 = 32x + -32x Combine like terms: 32x + -32x = 0 6 + -32x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -16x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -16x + x2)' equal to zero and attempt to solve: Simplifying 3 + -16x + x2 = 0 Solving 3 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -16x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -16x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -16x + x2 = 0 + -3 -16x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -16x + x2 = -3 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -3 + 64 Reorder the terms: 64 + -16x + x2 = -3 + 64 Combine like terms: -3 + 64 = 61 64 + -16x + x2 = 61 Factor a perfect square on the left side: (x + -8)(x + -8) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (x + -8) equal to 7.810249676 and -7.810249676.Subproblem 1
x + -8 = 7.810249676 Simplifying x + -8 = 7.810249676 Reorder the terms: -8 + x = 7.810249676 Solving -8 + x = 7.810249676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 7.810249676 + 8 Combine like terms: -8 + 8 = 0 0 + x = 7.810249676 + 8 x = 7.810249676 + 8 Combine like terms: 7.810249676 + 8 = 15.810249676 x = 15.810249676 Simplifying x = 15.810249676Subproblem 2
x + -8 = -7.810249676 Simplifying x + -8 = -7.810249676 Reorder the terms: -8 + x = -7.810249676 Solving -8 + x = -7.810249676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -7.810249676 + 8 Combine like terms: -8 + 8 = 0 0 + x = -7.810249676 + 8 x = -7.810249676 + 8 Combine like terms: -7.810249676 + 8 = 0.189750324 x = 0.189750324 Simplifying x = 0.189750324Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.810249676, 0.189750324}Solution
x = {15.810249676, 0.189750324}
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