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Simplifying -24x2 + 332x + -134 = 0 Reorder the terms: -134 + 332x + -24x2 = 0 Solving -134 + 332x + -24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-67 + 166x + -12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-67 + 166x + -12x2)' equal to zero and attempt to solve: Simplifying -67 + 166x + -12x2 = 0 Solving -67 + 166x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. 5.583333333 + -13.83333333x + x2 = 0 Move the constant term to the right: Add '-5.583333333' to each side of the equation. 5.583333333 + -13.83333333x + -5.583333333 + x2 = 0 + -5.583333333 Reorder the terms: 5.583333333 + -5.583333333 + -13.83333333x + x2 = 0 + -5.583333333 Combine like terms: 5.583333333 + -5.583333333 = 0.000000000 0.000000000 + -13.83333333x + x2 = 0 + -5.583333333 -13.83333333x + x2 = 0 + -5.583333333 Combine like terms: 0 + -5.583333333 = -5.583333333 -13.83333333x + x2 = -5.583333333 The x term is -13.83333333x. Take half its coefficient (-6.916666665). Square it (47.84027775) and add it to both sides. Add '47.84027775' to each side of the equation. -13.83333333x + 47.84027775 + x2 = -5.583333333 + 47.84027775 Reorder the terms: 47.84027775 + -13.83333333x + x2 = -5.583333333 + 47.84027775 Combine like terms: -5.583333333 + 47.84027775 = 42.256944417 47.84027775 + -13.83333333x + x2 = 42.256944417 Factor a perfect square on the left side: (x + -6.916666665)(x + -6.916666665) = 42.256944417 Calculate the square root of the right side: 6.500534164 Break this problem into two subproblems by setting (x + -6.916666665) equal to 6.500534164 and -6.500534164.Subproblem 1
x + -6.916666665 = 6.500534164 Simplifying x + -6.916666665 = 6.500534164 Reorder the terms: -6.916666665 + x = 6.500534164 Solving -6.916666665 + x = 6.500534164 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.916666665' to each side of the equation. -6.916666665 + 6.916666665 + x = 6.500534164 + 6.916666665 Combine like terms: -6.916666665 + 6.916666665 = 0.000000000 0.000000000 + x = 6.500534164 + 6.916666665 x = 6.500534164 + 6.916666665 Combine like terms: 6.500534164 + 6.916666665 = 13.417200829 x = 13.417200829 Simplifying x = 13.417200829Subproblem 2
x + -6.916666665 = -6.500534164 Simplifying x + -6.916666665 = -6.500534164 Reorder the terms: -6.916666665 + x = -6.500534164 Solving -6.916666665 + x = -6.500534164 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.916666665' to each side of the equation. -6.916666665 + 6.916666665 + x = -6.500534164 + 6.916666665 Combine like terms: -6.916666665 + 6.916666665 = 0.000000000 0.000000000 + x = -6.500534164 + 6.916666665 x = -6.500534164 + 6.916666665 Combine like terms: -6.500534164 + 6.916666665 = 0.416132501 x = 0.416132501 Simplifying x = 0.416132501Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.417200829, 0.416132501}Solution
x = {13.417200829, 0.416132501}
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