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Simplifying 2x2 + 2x2 + 2 = 2x + 68 Reorder the terms: 2 + 2x2 + 2x2 = 2x + 68 Combine like terms: 2x2 + 2x2 = 4x2 2 + 4x2 = 2x + 68 Reorder the terms: 2 + 4x2 = 68 + 2x Solving 2 + 4x2 = 68 + 2x Solving for variable 'x'. Reorder the terms: 2 + -68 + -2x + 4x2 = 68 + 2x + -68 + -2x Combine like terms: 2 + -68 = -66 -66 + -2x + 4x2 = 68 + 2x + -68 + -2x Reorder the terms: -66 + -2x + 4x2 = 68 + -68 + 2x + -2x Combine like terms: 68 + -68 = 0 -66 + -2x + 4x2 = 0 + 2x + -2x -66 + -2x + 4x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -66 + -2x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-33 + -1x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-33 + -1x + 2x2)' equal to zero and attempt to solve: Simplifying -33 + -1x + 2x2 = 0 Solving -33 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -16.5 + -0.5x + x2 = 0 Move the constant term to the right: Add '16.5' to each side of the equation. -16.5 + -0.5x + 16.5 + x2 = 0 + 16.5 Reorder the terms: -16.5 + 16.5 + -0.5x + x2 = 0 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + -0.5x + x2 = 0 + 16.5 -0.5x + x2 = 0 + 16.5 Combine like terms: 0 + 16.5 = 16.5 -0.5x + x2 = 16.5 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 16.5 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 16.5 + 0.0625 Combine like terms: 16.5 + 0.0625 = 16.5625 0.0625 + -0.5x + x2 = 16.5625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 16.5625 Calculate the square root of the right side: 4.069705149 Break this problem into two subproblems by setting (x + -0.25) equal to 4.069705149 and -4.069705149.Subproblem 1
x + -0.25 = 4.069705149 Simplifying x + -0.25 = 4.069705149 Reorder the terms: -0.25 + x = 4.069705149 Solving -0.25 + x = 4.069705149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 4.069705149 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 4.069705149 + 0.25 x = 4.069705149 + 0.25 Combine like terms: 4.069705149 + 0.25 = 4.319705149 x = 4.319705149 Simplifying x = 4.319705149Subproblem 2
x + -0.25 = -4.069705149 Simplifying x + -0.25 = -4.069705149 Reorder the terms: -0.25 + x = -4.069705149 Solving -0.25 + x = -4.069705149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -4.069705149 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -4.069705149 + 0.25 x = -4.069705149 + 0.25 Combine like terms: -4.069705149 + 0.25 = -3.819705149 x = -3.819705149 Simplifying x = -3.819705149Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.319705149, -3.819705149}Solution
x = {4.319705149, -3.819705149}
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