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Simplifying 36x2 + 48x + 10 = 0 Reorder the terms: 10 + 48x + 36x2 = 0 Solving 10 + 48x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 24x + 18x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 24x + 18x2)' equal to zero and attempt to solve: Simplifying 5 + 24x + 18x2 = 0 Solving 5 + 24x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.2777777778 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '-0.2777777778' to each side of the equation. 0.2777777778 + 1.333333333x + -0.2777777778 + x2 = 0 + -0.2777777778 Reorder the terms: 0.2777777778 + -0.2777777778 + 1.333333333x + x2 = 0 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + 1.333333333x + x2 = 0 + -0.2777777778 1.333333333x + x2 = 0 + -0.2777777778 Combine like terms: 0 + -0.2777777778 = -0.2777777778 1.333333333x + x2 = -0.2777777778 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 = -0.2777777778 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = -0.2777777778 + 0.4444444442 Combine like terms: -0.2777777778 + 0.4444444442 = 0.1666666664 0.4444444442 + 1.333333333x + x2 = 0.1666666664 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 0.1666666664 Calculate the square root of the right side: 0.40824829 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 0.40824829 and -0.40824829.Subproblem 1
x + 0.6666666665 = 0.40824829 Simplifying x + 0.6666666665 = 0.40824829 Reorder the terms: 0.6666666665 + x = 0.40824829 Solving 0.6666666665 + x = 0.40824829 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 = 0.40824829 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 0.40824829 + -0.6666666665 x = 0.40824829 + -0.6666666665 Combine like terms: 0.40824829 + -0.6666666665 = -0.2584183765 x = -0.2584183765 Simplifying x = -0.2584183765Subproblem 2
x + 0.6666666665 = -0.40824829 Simplifying x + 0.6666666665 = -0.40824829 Reorder the terms: 0.6666666665 + x = -0.40824829 Solving 0.6666666665 + x = -0.40824829 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 = -0.40824829 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -0.40824829 + -0.6666666665 x = -0.40824829 + -0.6666666665 Combine like terms: -0.40824829 + -0.6666666665 = -1.0749149565 x = -1.0749149565 Simplifying x = -1.0749149565Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.2584183765, -1.0749149565}Solution
x = {-0.2584183765, -1.0749149565}
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