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Simplifying 24x(3x + 4) = 10 Reorder the terms: 24x(4 + 3x) = 10 (4 * 24x + 3x * 24x) = 10 (96x + 72x2) = 10 Solving 96x + 72x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + 96x + 72x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 96x + 72x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 48x + 36x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 48x + 36x2)' equal to zero and attempt to solve: Simplifying -5 + 48x + 36x2 = 0 Solving -5 + 48x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.1388888889 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '0.1388888889' to each side of the equation. -0.1388888889 + 1.333333333x + 0.1388888889 + x2 = 0 + 0.1388888889 Reorder the terms: -0.1388888889 + 0.1388888889 + 1.333333333x + x2 = 0 + 0.1388888889 Combine like terms: -0.1388888889 + 0.1388888889 = 0.0000000000 0.0000000000 + 1.333333333x + x2 = 0 + 0.1388888889 1.333333333x + x2 = 0 + 0.1388888889 Combine like terms: 0 + 0.1388888889 = 0.1388888889 1.333333333x + x2 = 0.1388888889 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 = 0.1388888889 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 0.1388888889 + 0.4444444442 Combine like terms: 0.1388888889 + 0.4444444442 = 0.5833333331 0.4444444442 + 1.333333333x + x2 = 0.5833333331 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 0.5833333331 Calculate the square root of the right side: 0.763762616 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 0.763762616 and -0.763762616.Subproblem 1
x + 0.6666666665 = 0.763762616 Simplifying x + 0.6666666665 = 0.763762616 Reorder the terms: 0.6666666665 + x = 0.763762616 Solving 0.6666666665 + x = 0.763762616 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 = 0.763762616 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 0.763762616 + -0.6666666665 x = 0.763762616 + -0.6666666665 Combine like terms: 0.763762616 + -0.6666666665 = 0.0970959495 x = 0.0970959495 Simplifying x = 0.0970959495Subproblem 2
x + 0.6666666665 = -0.763762616 Simplifying x + 0.6666666665 = -0.763762616 Reorder the terms: 0.6666666665 + x = -0.763762616 Solving 0.6666666665 + x = -0.763762616 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 = -0.763762616 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -0.763762616 + -0.6666666665 x = -0.763762616 + -0.6666666665 Combine like terms: -0.763762616 + -0.6666666665 = -1.4304292825 x = -1.4304292825 Simplifying x = -1.4304292825Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0970959495, -1.4304292825}Solution
x = {0.0970959495, -1.4304292825}
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