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Simplifying 0 = 12x2 + -160x + 120 Reorder the terms: 0 = 120 + -160x + 12x2 Solving 0 = 120 + -160x + 12x2 Solving for variable 'x'. Combine like terms: 0 + -120 = -120 -120 + 160x + -12x2 = 120 + -160x + 12x2 + -120 + 160x + -12x2 Reorder the terms: -120 + 160x + -12x2 = 120 + -120 + -160x + 160x + 12x2 + -12x2 Combine like terms: 120 + -120 = 0 -120 + 160x + -12x2 = 0 + -160x + 160x + 12x2 + -12x2 -120 + 160x + -12x2 = -160x + 160x + 12x2 + -12x2 Combine like terms: -160x + 160x = 0 -120 + 160x + -12x2 = 0 + 12x2 + -12x2 -120 + 160x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -120 + 160x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-30 + 40x + -3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-30 + 40x + -3x2)' equal to zero and attempt to solve: Simplifying -30 + 40x + -3x2 = 0 Solving -30 + 40x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 10 + -13.33333333x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -13.33333333x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -13.33333333x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -13.33333333x + x2 = 0 + -10 -13.33333333x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -13.33333333x + x2 = -10 The x term is -13.33333333x. Take half its coefficient (-6.666666665). Square it (44.44444442) and add it to both sides. Add '44.44444442' to each side of the equation. -13.33333333x + 44.44444442 + x2 = -10 + 44.44444442 Reorder the terms: 44.44444442 + -13.33333333x + x2 = -10 + 44.44444442 Combine like terms: -10 + 44.44444442 = 34.44444442 44.44444442 + -13.33333333x + x2 = 34.44444442 Factor a perfect square on the left side: (x + -6.666666665)(x + -6.666666665) = 34.44444442 Calculate the square root of the right side: 5.868938952 Break this problem into two subproblems by setting (x + -6.666666665) equal to 5.868938952 and -5.868938952.Subproblem 1
x + -6.666666665 = 5.868938952 Simplifying x + -6.666666665 = 5.868938952 Reorder the terms: -6.666666665 + x = 5.868938952 Solving -6.666666665 + x = 5.868938952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.666666665' to each side of the equation. -6.666666665 + 6.666666665 + x = 5.868938952 + 6.666666665 Combine like terms: -6.666666665 + 6.666666665 = 0.000000000 0.000000000 + x = 5.868938952 + 6.666666665 x = 5.868938952 + 6.666666665 Combine like terms: 5.868938952 + 6.666666665 = 12.535605617 x = 12.535605617 Simplifying x = 12.535605617Subproblem 2
x + -6.666666665 = -5.868938952 Simplifying x + -6.666666665 = -5.868938952 Reorder the terms: -6.666666665 + x = -5.868938952 Solving -6.666666665 + x = -5.868938952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.666666665' to each side of the equation. -6.666666665 + 6.666666665 + x = -5.868938952 + 6.666666665 Combine like terms: -6.666666665 + 6.666666665 = 0.000000000 0.000000000 + x = -5.868938952 + 6.666666665 x = -5.868938952 + 6.666666665 Combine like terms: -5.868938952 + 6.666666665 = 0.797727713 x = 0.797727713 Simplifying x = 0.797727713Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.535605617, 0.797727713}Solution
x = {12.535605617, 0.797727713}
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