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Simplifying (2.3125)(x + -3.1875)(x) = 182.742 Reorder the terms: 2.3125(-3.1875 + x)(x) = 182.742 Reorder the terms for easier multiplication: 2.3125x(-3.1875 + x) = 182.742 (-3.1875 * 2.3125x + x * 2.3125x) = 182.742 (-7.37109375x + 2.3125x2) = 182.742 Solving -7.37109375x + 2.3125x2 = 182.742 Solving for variable 'x'. Reorder the terms: -182.742 + -7.37109375x + 2.3125x2 = 182.742 + -182.742 Combine like terms: 182.742 + -182.742 = 0.000 -182.742 + -7.37109375x + 2.3125x2 = 0.000 Begin completing the square. Divide all terms by 2.3125 the coefficient of the squared term: Divide each side by '2.3125'. -79.02356757 + -3.1875x + x2 = 0 Move the constant term to the right: Add '79.02356757' to each side of the equation. -79.02356757 + -3.1875x + 79.02356757 + x2 = 0 + 79.02356757 Reorder the terms: -79.02356757 + 79.02356757 + -3.1875x + x2 = 0 + 79.02356757 Combine like terms: -79.02356757 + 79.02356757 = 0.00000000 0.00000000 + -3.1875x + x2 = 0 + 79.02356757 -3.1875x + x2 = 0 + 79.02356757 Combine like terms: 0 + 79.02356757 = 79.02356757 -3.1875x + x2 = 79.02356757 The x term is -3.1875x. Take half its coefficient (-1.59375). Square it (2.540039063) and add it to both sides. Add '2.540039063' to each side of the equation. -3.1875x + 2.540039063 + x2 = 79.02356757 + 2.540039063 Reorder the terms: 2.540039063 + -3.1875x + x2 = 79.02356757 + 2.540039063 Combine like terms: 79.02356757 + 2.540039063 = 81.563606633 2.540039063 + -3.1875x + x2 = 81.563606633 Factor a perfect square on the left side: (x + -1.59375)(x + -1.59375) = 81.563606633 Calculate the square root of the right side: 9.031257201 Break this problem into two subproblems by setting (x + -1.59375) equal to 9.031257201 and -9.031257201.Subproblem 1
x + -1.59375 = 9.031257201 Simplifying x + -1.59375 = 9.031257201 Reorder the terms: -1.59375 + x = 9.031257201 Solving -1.59375 + x = 9.031257201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.59375' to each side of the equation. -1.59375 + 1.59375 + x = 9.031257201 + 1.59375 Combine like terms: -1.59375 + 1.59375 = 0.00000 0.00000 + x = 9.031257201 + 1.59375 x = 9.031257201 + 1.59375 Combine like terms: 9.031257201 + 1.59375 = 10.625007201 x = 10.625007201 Simplifying x = 10.625007201Subproblem 2
x + -1.59375 = -9.031257201 Simplifying x + -1.59375 = -9.031257201 Reorder the terms: -1.59375 + x = -9.031257201 Solving -1.59375 + x = -9.031257201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.59375' to each side of the equation. -1.59375 + 1.59375 + x = -9.031257201 + 1.59375 Combine like terms: -1.59375 + 1.59375 = 0.00000 0.00000 + x = -9.031257201 + 1.59375 x = -9.031257201 + 1.59375 Combine like terms: -9.031257201 + 1.59375 = -7.437507201 x = -7.437507201 Simplifying x = -7.437507201Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.625007201, -7.437507201}
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