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Simplifying 8x2 + -24x = -13 Reorder the terms: -24x + 8x2 = -13 Solving -24x + 8x2 = -13 Solving for variable 'x'. Reorder the terms: 13 + -24x + 8x2 = -13 + 13 Combine like terms: -13 + 13 = 0 13 + -24x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.625 + -3x + x2 = 0 Move the constant term to the right: Add '-1.625' to each side of the equation. 1.625 + -3x + -1.625 + x2 = 0 + -1.625 Reorder the terms: 1.625 + -1.625 + -3x + x2 = 0 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + -3x + x2 = 0 + -1.625 -3x + x2 = 0 + -1.625 Combine like terms: 0 + -1.625 = -1.625 -3x + x2 = -1.625 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -1.625 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -1.625 + 2.25 Combine like terms: -1.625 + 2.25 = 0.625 2.25 + -3x + x2 = 0.625 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 0.625 Calculate the square root of the right side: 0.790569415 Break this problem into two subproblems by setting (x + -1.5) equal to 0.790569415 and -0.790569415.Subproblem 1
x + -1.5 = 0.790569415 Simplifying x + -1.5 = 0.790569415 Reorder the terms: -1.5 + x = 0.790569415 Solving -1.5 + x = 0.790569415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 0.790569415 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 0.790569415 + 1.5 x = 0.790569415 + 1.5 Combine like terms: 0.790569415 + 1.5 = 2.290569415 x = 2.290569415 Simplifying x = 2.290569415Subproblem 2
x + -1.5 = -0.790569415 Simplifying x + -1.5 = -0.790569415 Reorder the terms: -1.5 + x = -0.790569415 Solving -1.5 + x = -0.790569415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -0.790569415 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -0.790569415 + 1.5 x = -0.790569415 + 1.5 Combine like terms: -0.790569415 + 1.5 = 0.709430585 x = 0.709430585 Simplifying x = 0.709430585Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.290569415, 0.709430585}
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