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Simplifying 36x2 + -624x + 880 = 0 Reorder the terms: 880 + -624x + 36x2 = 0 Solving 880 + -624x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(220 + -156x + 9x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(220 + -156x + 9x2)' equal to zero and attempt to solve: Simplifying 220 + -156x + 9x2 = 0 Solving 220 + -156x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 24.44444444 + -17.33333333x + x2 = 0 Move the constant term to the right: Add '-24.44444444' to each side of the equation. 24.44444444 + -17.33333333x + -24.44444444 + x2 = 0 + -24.44444444 Reorder the terms: 24.44444444 + -24.44444444 + -17.33333333x + x2 = 0 + -24.44444444 Combine like terms: 24.44444444 + -24.44444444 = 0.00000000 0.00000000 + -17.33333333x + x2 = 0 + -24.44444444 -17.33333333x + x2 = 0 + -24.44444444 Combine like terms: 0 + -24.44444444 = -24.44444444 -17.33333333x + x2 = -24.44444444 The x term is -17.33333333x. Take half its coefficient (-8.666666665). Square it (75.11111108) and add it to both sides. Add '75.11111108' to each side of the equation. -17.33333333x + 75.11111108 + x2 = -24.44444444 + 75.11111108 Reorder the terms: 75.11111108 + -17.33333333x + x2 = -24.44444444 + 75.11111108 Combine like terms: -24.44444444 + 75.11111108 = 50.66666664 75.11111108 + -17.33333333x + x2 = 50.66666664 Factor a perfect square on the left side: (x + -8.666666665)(x + -8.666666665) = 50.66666664 Calculate the square root of the right side: 7.118052166 Break this problem into two subproblems by setting (x + -8.666666665) equal to 7.118052166 and -7.118052166.Subproblem 1
x + -8.666666665 = 7.118052166 Simplifying x + -8.666666665 = 7.118052166 Reorder the terms: -8.666666665 + x = 7.118052166 Solving -8.666666665 + x = 7.118052166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.666666665' to each side of the equation. -8.666666665 + 8.666666665 + x = 7.118052166 + 8.666666665 Combine like terms: -8.666666665 + 8.666666665 = 0.000000000 0.000000000 + x = 7.118052166 + 8.666666665 x = 7.118052166 + 8.666666665 Combine like terms: 7.118052166 + 8.666666665 = 15.784718831 x = 15.784718831 Simplifying x = 15.784718831Subproblem 2
x + -8.666666665 = -7.118052166 Simplifying x + -8.666666665 = -7.118052166 Reorder the terms: -8.666666665 + x = -7.118052166 Solving -8.666666665 + x = -7.118052166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.666666665' to each side of the equation. -8.666666665 + 8.666666665 + x = -7.118052166 + 8.666666665 Combine like terms: -8.666666665 + 8.666666665 = 0.000000000 0.000000000 + x = -7.118052166 + 8.666666665 x = -7.118052166 + 8.666666665 Combine like terms: -7.118052166 + 8.666666665 = 1.548614499 x = 1.548614499 Simplifying x = 1.548614499Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.784718831, 1.548614499}Solution
x = {15.784718831, 1.548614499}
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