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Simplifying 4x2 + -2x = 44 Reorder the terms: -2x + 4x2 = 44 Solving -2x + 4x2 = 44 Solving for variable 'x'. Reorder the terms: -44 + -2x + 4x2 = 44 + -44 Combine like terms: 44 + -44 = 0 -44 + -2x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-22 + -1x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-22 + -1x + 2x2)' equal to zero and attempt to solve: Simplifying -22 + -1x + 2x2 = 0 Solving -22 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -11 + -0.5x + x2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + -0.5x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -0.5x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -0.5x + x2 = 0 + 11 -0.5x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -0.5x + x2 = 11 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 = 11 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 11 + 0.0625 Combine like terms: 11 + 0.0625 = 11.0625 0.0625 + -0.5x + x2 = 11.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 11.0625 Calculate the square root of the right side: 3.326033674 Break this problem into two subproblems by setting (x + -0.25) equal to 3.326033674 and -3.326033674.Subproblem 1
x + -0.25 = 3.326033674 Simplifying x + -0.25 = 3.326033674 Reorder the terms: -0.25 + x = 3.326033674 Solving -0.25 + x = 3.326033674 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 = 3.326033674 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 3.326033674 + 0.25 x = 3.326033674 + 0.25 Combine like terms: 3.326033674 + 0.25 = 3.576033674 x = 3.576033674 Simplifying x = 3.576033674Subproblem 2
x + -0.25 = -3.326033674 Simplifying x + -0.25 = -3.326033674 Reorder the terms: -0.25 + x = -3.326033674 Solving -0.25 + x = -3.326033674 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 = -3.326033674 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -3.326033674 + 0.25 x = -3.326033674 + 0.25 Combine like terms: -3.326033674 + 0.25 = -3.076033674 x = -3.076033674 Simplifying x = -3.076033674Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.576033674, -3.076033674}Solution
x = {3.576033674, -3.076033674}
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