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Simplifying 36x2 + 48x + 14 = 0 Reorder the terms: 14 + 48x + 36x2 = 0 Solving 14 + 48x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + 24x + 18x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + 24x + 18x2)' equal to zero and attempt to solve: Simplifying 7 + 24x + 18x2 = 0 Solving 7 + 24x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.3888888889 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '-0.3888888889' to each side of the equation. 0.3888888889 + 1.333333333x + -0.3888888889 + x2 = 0 + -0.3888888889 Reorder the terms: 0.3888888889 + -0.3888888889 + 1.333333333x + x2 = 0 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + 1.333333333x + x2 = 0 + -0.3888888889 1.333333333x + x2 = 0 + -0.3888888889 Combine like terms: 0 + -0.3888888889 = -0.3888888889 1.333333333x + x2 = -0.3888888889 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = -0.3888888889 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = -0.3888888889 + 0.4444444442 Combine like terms: -0.3888888889 + 0.4444444442 = 0.0555555553 0.4444444442 + 1.333333333x + x2 = 0.0555555553 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 0.0555555553 Calculate the square root of the right side: 0.23570226 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 0.23570226 and -0.23570226.Subproblem 1
x + 0.6666666665 = 0.23570226 Simplifying x + 0.6666666665 = 0.23570226 Reorder the terms: 0.6666666665 + x = 0.23570226 Solving 0.6666666665 + x = 0.23570226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 0.23570226 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 0.23570226 + -0.6666666665 x = 0.23570226 + -0.6666666665 Combine like terms: 0.23570226 + -0.6666666665 = -0.4309644065 x = -0.4309644065 Simplifying x = -0.4309644065Subproblem 2
x + 0.6666666665 = -0.23570226 Simplifying x + 0.6666666665 = -0.23570226 Reorder the terms: 0.6666666665 + x = -0.23570226 Solving 0.6666666665 + x = -0.23570226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -0.23570226 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -0.23570226 + -0.6666666665 x = -0.23570226 + -0.6666666665 Combine like terms: -0.23570226 + -0.6666666665 = -0.9023689265 x = -0.9023689265 Simplifying x = -0.9023689265Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.4309644065, -0.9023689265}Solution
x = {-0.4309644065, -0.9023689265}
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