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Simplifying 12x2 + -172x + 120 = 0 Reorder the terms: 120 + -172x + 12x2 = 0 Solving 120 + -172x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(30 + -43x + 3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(30 + -43x + 3x2)' equal to zero and attempt to solve: Simplifying 30 + -43x + 3x2 = 0 Solving 30 + -43x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 10 + -14.33333333x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -14.33333333x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -14.33333333x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -14.33333333x + x2 = 0 + -10 -14.33333333x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -14.33333333x + x2 = -10 The x term is -14.33333333x. Take half its coefficient (-7.166666665). Square it (51.36111109) and add it to both sides. Add '51.36111109' to each side of the equation. -14.33333333x + 51.36111109 + x2 = -10 + 51.36111109 Reorder the terms: 51.36111109 + -14.33333333x + x2 = -10 + 51.36111109 Combine like terms: -10 + 51.36111109 = 41.36111109 51.36111109 + -14.33333333x + x2 = 41.36111109 Factor a perfect square on the left side: (x + -7.166666665)(x + -7.166666665) = 41.36111109 Calculate the square root of the right side: 6.431260459 Break this problem into two subproblems by setting (x + -7.166666665) equal to 6.431260459 and -6.431260459.Subproblem 1
x + -7.166666665 = 6.431260459 Simplifying x + -7.166666665 = 6.431260459 Reorder the terms: -7.166666665 + x = 6.431260459 Solving -7.166666665 + x = 6.431260459 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.166666665' to each side of the equation. -7.166666665 + 7.166666665 + x = 6.431260459 + 7.166666665 Combine like terms: -7.166666665 + 7.166666665 = 0.000000000 0.000000000 + x = 6.431260459 + 7.166666665 x = 6.431260459 + 7.166666665 Combine like terms: 6.431260459 + 7.166666665 = 13.597927124 x = 13.597927124 Simplifying x = 13.597927124Subproblem 2
x + -7.166666665 = -6.431260459 Simplifying x + -7.166666665 = -6.431260459 Reorder the terms: -7.166666665 + x = -6.431260459 Solving -7.166666665 + x = -6.431260459 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.166666665' to each side of the equation. -7.166666665 + 7.166666665 + x = -6.431260459 + 7.166666665 Combine like terms: -7.166666665 + 7.166666665 = 0.000000000 0.000000000 + x = -6.431260459 + 7.166666665 x = -6.431260459 + 7.166666665 Combine like terms: -6.431260459 + 7.166666665 = 0.735406206 x = 0.735406206 Simplifying x = 0.735406206Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.597927124, 0.735406206}Solution
x = {13.597927124, 0.735406206}
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