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Simplifying -24x2 + -15 = 39x + -2 Reorder the terms: -15 + -24x2 = 39x + -2 Reorder the terms: -15 + -24x2 = -2 + 39x Solving -15 + -24x2 = -2 + 39x Solving for variable 'x'. Reorder the terms: -15 + 2 + -39x + -24x2 = -2 + 39x + 2 + -39x Combine like terms: -15 + 2 = -13 -13 + -39x + -24x2 = -2 + 39x + 2 + -39x Reorder the terms: -13 + -39x + -24x2 = -2 + 2 + 39x + -39x Combine like terms: -2 + 2 = 0 -13 + -39x + -24x2 = 0 + 39x + -39x -13 + -39x + -24x2 = 39x + -39x Combine like terms: 39x + -39x = 0 -13 + -39x + -24x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(13 + 39x + 24x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(13 + 39x + 24x2)' equal to zero and attempt to solve: Simplifying 13 + 39x + 24x2 = 0 Solving 13 + 39x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. 0.5416666667 + 1.625x + x2 = 0 Move the constant term to the right: Add '-0.5416666667' to each side of the equation. 0.5416666667 + 1.625x + -0.5416666667 + x2 = 0 + -0.5416666667 Reorder the terms: 0.5416666667 + -0.5416666667 + 1.625x + x2 = 0 + -0.5416666667 Combine like terms: 0.5416666667 + -0.5416666667 = 0.0000000000 0.0000000000 + 1.625x + x2 = 0 + -0.5416666667 1.625x + x2 = 0 + -0.5416666667 Combine like terms: 0 + -0.5416666667 = -0.5416666667 1.625x + x2 = -0.5416666667 The x term is 1.625x. Take half its coefficient (0.8125). Square it (0.66015625) and add it to both sides. Add '0.66015625' to each side of the equation. 1.625x + 0.66015625 + x2 = -0.5416666667 + 0.66015625 Reorder the terms: 0.66015625 + 1.625x + x2 = -0.5416666667 + 0.66015625 Combine like terms: -0.5416666667 + 0.66015625 = 0.1184895833 0.66015625 + 1.625x + x2 = 0.1184895833 Factor a perfect square on the left side: (x + 0.8125)(x + 0.8125) = 0.1184895833 Calculate the square root of the right side: 0.344223159 Break this problem into two subproblems by setting (x + 0.8125) equal to 0.344223159 and -0.344223159.Subproblem 1
x + 0.8125 = 0.344223159 Simplifying x + 0.8125 = 0.344223159 Reorder the terms: 0.8125 + x = 0.344223159 Solving 0.8125 + x = 0.344223159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8125' to each side of the equation. 0.8125 + -0.8125 + x = 0.344223159 + -0.8125 Combine like terms: 0.8125 + -0.8125 = 0.0000 0.0000 + x = 0.344223159 + -0.8125 x = 0.344223159 + -0.8125 Combine like terms: 0.344223159 + -0.8125 = -0.468276841 x = -0.468276841 Simplifying x = -0.468276841Subproblem 2
x + 0.8125 = -0.344223159 Simplifying x + 0.8125 = -0.344223159 Reorder the terms: 0.8125 + x = -0.344223159 Solving 0.8125 + x = -0.344223159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8125' to each side of the equation. 0.8125 + -0.8125 + x = -0.344223159 + -0.8125 Combine like terms: 0.8125 + -0.8125 = 0.0000 0.0000 + x = -0.344223159 + -0.8125 x = -0.344223159 + -0.8125 Combine like terms: -0.344223159 + -0.8125 = -1.156723159 x = -1.156723159 Simplifying x = -1.156723159Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.468276841, -1.156723159}Solution
x = {-0.468276841, -1.156723159}
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