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Simplifying 2x2 + -48x + 6 = 0 Reorder the terms: 6 + -48x + 2x2 = 0 Solving 6 + -48x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -24x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -24x + x2)' equal to zero and attempt to solve: Simplifying 3 + -24x + x2 = 0 Solving 3 + -24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -24x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -24x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -24x + x2 = 0 + -3 -24x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -24x + x2 = -3 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -3 + 144 Reorder the terms: 144 + -24x + x2 = -3 + 144 Combine like terms: -3 + 144 = 141 144 + -24x + x2 = 141 Factor a perfect square on the left side: (x + -12)(x + -12) = 141 Calculate the square root of the right side: 11.874342087 Break this problem into two subproblems by setting (x + -12) equal to 11.874342087 and -11.874342087.Subproblem 1
x + -12 = 11.874342087 Simplifying x + -12 = 11.874342087 Reorder the terms: -12 + x = 11.874342087 Solving -12 + x = 11.874342087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 11.874342087 + 12 Combine like terms: -12 + 12 = 0 0 + x = 11.874342087 + 12 x = 11.874342087 + 12 Combine like terms: 11.874342087 + 12 = 23.874342087 x = 23.874342087 Simplifying x = 23.874342087Subproblem 2
x + -12 = -11.874342087 Simplifying x + -12 = -11.874342087 Reorder the terms: -12 + x = -11.874342087 Solving -12 + x = -11.874342087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -11.874342087 + 12 Combine like terms: -12 + 12 = 0 0 + x = -11.874342087 + 12 x = -11.874342087 + 12 Combine like terms: -11.874342087 + 12 = 0.125657913 x = 0.125657913 Simplifying x = 0.125657913Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.874342087, 0.125657913}Solution
x = {23.874342087, 0.125657913}
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