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Simplifying 2x2 + -38x + 12 = 0 Reorder the terms: 12 + -38x + 2x2 = 0 Solving 12 + -38x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -19x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -19x + x2)' equal to zero and attempt to solve: Simplifying 6 + -19x + x2 = 0 Solving 6 + -19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -19x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -19x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -19x + x2 = 0 + -6 -19x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -19x + x2 = -6 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = -6 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -6 + 90.25 Combine like terms: -6 + 90.25 = 84.25 90.25 + -19x + x2 = 84.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 84.25 Calculate the square root of the right side: 9.178779875 Break this problem into two subproblems by setting (x + -9.5) equal to 9.178779875 and -9.178779875.Subproblem 1
x + -9.5 = 9.178779875 Simplifying x + -9.5 = 9.178779875 Reorder the terms: -9.5 + x = 9.178779875 Solving -9.5 + x = 9.178779875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 9.178779875 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 9.178779875 + 9.5 x = 9.178779875 + 9.5 Combine like terms: 9.178779875 + 9.5 = 18.678779875 x = 18.678779875 Simplifying x = 18.678779875Subproblem 2
x + -9.5 = -9.178779875 Simplifying x + -9.5 = -9.178779875 Reorder the terms: -9.5 + x = -9.178779875 Solving -9.5 + x = -9.178779875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -9.178779875 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -9.178779875 + 9.5 x = -9.178779875 + 9.5 Combine like terms: -9.178779875 + 9.5 = 0.321220125 x = 0.321220125 Simplifying x = 0.321220125Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.678779875, 0.321220125}Solution
x = {18.678779875, 0.321220125}
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