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Simplifying 24(2x2 + x + -182) = 0 Reorder the terms: 24(-182 + x + 2x2) = 0 (-182 * 24 + x * 24 + 2x2 * 24) = 0 (-4368 + 24x + 48x2) = 0 Solving -4368 + 24x + 48x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '24'. 24(-182 + x + 2x2) = 0 Ignore the factor 24.Subproblem 1
Set the factor '(-182 + x + 2x2)' equal to zero and attempt to solve: Simplifying -182 + x + 2x2 = 0 Solving -182 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -91 + 0.5x + x2 = 0 Move the constant term to the right: Add '91' to each side of the equation. -91 + 0.5x + 91 + x2 = 0 + 91 Reorder the terms: -91 + 91 + 0.5x + x2 = 0 + 91 Combine like terms: -91 + 91 = 0 0 + 0.5x + x2 = 0 + 91 0.5x + x2 = 0 + 91 Combine like terms: 0 + 91 = 91 0.5x + x2 = 91 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5x + 0.25 + x2 = 91 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 91 + 0.25 Combine like terms: 91 + 0.25 = 91.25 0.25 + 0.5x + x2 = 91.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 91.25 Calculate the square root of the right side: 9.552486587 Break this problem into two subproblems by setting (x + 0.5) equal to 9.552486587 and -9.552486587.Subproblem 1
x + 0.5 = 9.552486587 Simplifying x + 0.5 = 9.552486587 Reorder the terms: 0.5 + x = 9.552486587 Solving 0.5 + x = 9.552486587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 9.552486587 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 9.552486587 + -0.5 x = 9.552486587 + -0.5 Combine like terms: 9.552486587 + -0.5 = 9.052486587 x = 9.052486587 Simplifying x = 9.052486587Subproblem 2
x + 0.5 = -9.552486587 Simplifying x + 0.5 = -9.552486587 Reorder the terms: 0.5 + x = -9.552486587 Solving 0.5 + x = -9.552486587 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -9.552486587 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -9.552486587 + -0.5 x = -9.552486587 + -0.5 Combine like terms: -9.552486587 + -0.5 = -10.052486587 x = -10.052486587 Simplifying x = -10.052486587Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.052486587, -10.052486587}Solution
x = {9.052486587, -10.052486587}
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