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Simplifying 0 = -1x2 + 18.843666x + 679.191375 Reorder the terms: 0 = 679.191375 + 18.843666x + -1x2 Solving 0 = 679.191375 + 18.843666x + -1x2 Solving for variable 'x'. Combine like terms: 0 + -679.191375 = -679.191375 -679.191375 + -18.843666x + x2 = 679.191375 + 18.843666x + -1x2 + -679.191375 + -18.843666x + x2 Reorder the terms: -679.191375 + -18.843666x + x2 = 679.191375 + -679.191375 + 18.843666x + -18.843666x + -1x2 + x2 Combine like terms: 679.191375 + -679.191375 = 0.000000 -679.191375 + -18.843666x + x2 = 0.000000 + 18.843666x + -18.843666x + -1x2 + x2 -679.191375 + -18.843666x + x2 = 18.843666x + -18.843666x + -1x2 + x2 Combine like terms: 18.843666x + -18.843666x = 0.000000 -679.191375 + -18.843666x + x2 = 0.000000 + -1x2 + x2 -679.191375 + -18.843666x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -679.191375 + -18.843666x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '679.191375' to each side of the equation. -679.191375 + -18.843666x + 679.191375 + x2 = 0 + 679.191375 Reorder the terms: -679.191375 + 679.191375 + -18.843666x + x2 = 0 + 679.191375 Combine like terms: -679.191375 + 679.191375 = 0.000000 0.000000 + -18.843666x + x2 = 0 + 679.191375 -18.843666x + x2 = 0 + 679.191375 Combine like terms: 0 + 679.191375 = 679.191375 -18.843666x + x2 = 679.191375 The x term is -18.843666x. Take half its coefficient (-9.421833). Square it (88.77093708) and add it to both sides. Add '88.77093708' to each side of the equation. -18.843666x + 88.77093708 + x2 = 679.191375 + 88.77093708 Reorder the terms: 88.77093708 + -18.843666x + x2 = 679.191375 + 88.77093708 Combine like terms: 679.191375 + 88.77093708 = 767.96231208 88.77093708 + -18.843666x + x2 = 767.96231208 Factor a perfect square on the left side: (x + -9.421833)(x + -9.421833) = 767.96231208 Calculate the square root of the right side: 27.71213294 Break this problem into two subproblems by setting (x + -9.421833) equal to 27.71213294 and -27.71213294.Subproblem 1
x + -9.421833 = 27.71213294 Simplifying x + -9.421833 = 27.71213294 Reorder the terms: -9.421833 + x = 27.71213294 Solving -9.421833 + x = 27.71213294 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.421833' to each side of the equation. -9.421833 + 9.421833 + x = 27.71213294 + 9.421833 Combine like terms: -9.421833 + 9.421833 = 0.000000 0.000000 + x = 27.71213294 + 9.421833 x = 27.71213294 + 9.421833 Combine like terms: 27.71213294 + 9.421833 = 37.13396594 x = 37.13396594 Simplifying x = 37.13396594Subproblem 2
x + -9.421833 = -27.71213294 Simplifying x + -9.421833 = -27.71213294 Reorder the terms: -9.421833 + x = -27.71213294 Solving -9.421833 + x = -27.71213294 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.421833' to each side of the equation. -9.421833 + 9.421833 + x = -27.71213294 + 9.421833 Combine like terms: -9.421833 + 9.421833 = 0.000000 0.000000 + x = -27.71213294 + 9.421833 x = -27.71213294 + 9.421833 Combine like terms: -27.71213294 + 9.421833 = -18.29029994 x = -18.29029994 Simplifying x = -18.29029994Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.13396594, -18.29029994}
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