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Simplifying 36x2 + 28x + -60 = 0 Reorder the terms: -60 + 28x + 36x2 = 0 Solving -60 + 28x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-15 + 7x + 9x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-15 + 7x + 9x2)' equal to zero and attempt to solve: Simplifying -15 + 7x + 9x2 = 0 Solving -15 + 7x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.666666667 + 0.7777777778x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + 0.7777777778x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + 0.7777777778x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + 0.7777777778x + x2 = 0 + 1.666666667 0.7777777778x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 0.7777777778x + x2 = 1.666666667 The x term is 0.7777777778x. Take half its coefficient (0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. 0.7777777778x + 0.1512345679 + x2 = 1.666666667 + 0.1512345679 Reorder the terms: 0.1512345679 + 0.7777777778x + x2 = 1.666666667 + 0.1512345679 Combine like terms: 1.666666667 + 0.1512345679 = 1.8179012349 0.1512345679 + 0.7777777778x + x2 = 1.8179012349 Factor a perfect square on the left side: (x + 0.3888888889)(x + 0.3888888889) = 1.8179012349 Calculate the square root of the right side: 1.348295678 Break this problem into two subproblems by setting (x + 0.3888888889) equal to 1.348295678 and -1.348295678.Subproblem 1
x + 0.3888888889 = 1.348295678 Simplifying x + 0.3888888889 = 1.348295678 Reorder the terms: 0.3888888889 + x = 1.348295678 Solving 0.3888888889 + x = 1.348295678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3888888889' to each side of the equation. 0.3888888889 + -0.3888888889 + x = 1.348295678 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = 1.348295678 + -0.3888888889 x = 1.348295678 + -0.3888888889 Combine like terms: 1.348295678 + -0.3888888889 = 0.9594067891 x = 0.9594067891 Simplifying x = 0.9594067891Subproblem 2
x + 0.3888888889 = -1.348295678 Simplifying x + 0.3888888889 = -1.348295678 Reorder the terms: 0.3888888889 + x = -1.348295678 Solving 0.3888888889 + x = -1.348295678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3888888889' to each side of the equation. 0.3888888889 + -0.3888888889 + x = -1.348295678 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = -1.348295678 + -0.3888888889 x = -1.348295678 + -0.3888888889 Combine like terms: -1.348295678 + -0.3888888889 = -1.7371845669 x = -1.7371845669 Simplifying x = -1.7371845669Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9594067891, -1.7371845669}Solution
x = {0.9594067891, -1.7371845669}
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