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Simplifying 13.740x2 + -250.245x + 1591.111 = 3499.47 Reorder the terms: 1591.111 + -250.245x + 13.740x2 = 3499.47 Solving 1591.111 + -250.245x + 13.740x2 = 3499.47 Solving for variable 'x'. Reorder the terms: 1591.111 + -3499.47 + -250.245x + 13.740x2 = 3499.47 + -3499.47 Combine like terms: 1591.111 + -3499.47 = -1908.359 -1908.359 + -250.245x + 13.740x2 = 3499.47 + -3499.47 Combine like terms: 3499.47 + -3499.47 = 0.00 -1908.359 + -250.245x + 13.740x2 = 0.00 Begin completing the square. Divide all terms by 13.740 the coefficient of the squared term: Divide each side by '13.740'. -138.8907569 + -18.2128821x + x2 = 0 Move the constant term to the right: Add '138.8907569' to each side of the equation. -138.8907569 + -18.2128821x + 138.8907569 + x2 = 0 + 138.8907569 Reorder the terms: -138.8907569 + 138.8907569 + -18.2128821x + x2 = 0 + 138.8907569 Combine like terms: -138.8907569 + 138.8907569 = 0.0000000 0.0000000 + -18.2128821x + x2 = 0 + 138.8907569 -18.2128821x + x2 = 0 + 138.8907569 Combine like terms: 0 + 138.8907569 = 138.8907569 -18.2128821x + x2 = 138.8907569 The x term is -18.2128821x. Take half its coefficient (-9.10644105). Square it (82.92726860) and add it to both sides. Add '82.92726860' to each side of the equation. -18.2128821x + 82.92726860 + x2 = 138.8907569 + 82.92726860 Reorder the terms: 82.92726860 + -18.2128821x + x2 = 138.8907569 + 82.92726860 Combine like terms: 138.8907569 + 82.92726860 = 221.8180255 82.92726860 + -18.2128821x + x2 = 221.8180255 Factor a perfect square on the left side: (x + -9.10644105)(x + -9.10644105) = 221.8180255 Calculate the square root of the right side: 14.893556509 Break this problem into two subproblems by setting (x + -9.10644105) equal to 14.893556509 and -14.893556509.Subproblem 1
x + -9.10644105 = 14.893556509 Simplifying x + -9.10644105 = 14.893556509 Reorder the terms: -9.10644105 + x = 14.893556509 Solving -9.10644105 + x = 14.893556509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.10644105' to each side of the equation. -9.10644105 + 9.10644105 + x = 14.893556509 + 9.10644105 Combine like terms: -9.10644105 + 9.10644105 = 0.00000000 0.00000000 + x = 14.893556509 + 9.10644105 x = 14.893556509 + 9.10644105 Combine like terms: 14.893556509 + 9.10644105 = 23.999997559 x = 23.999997559 Simplifying x = 23.999997559Subproblem 2
x + -9.10644105 = -14.893556509 Simplifying x + -9.10644105 = -14.893556509 Reorder the terms: -9.10644105 + x = -14.893556509 Solving -9.10644105 + x = -14.893556509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.10644105' to each side of the equation. -9.10644105 + 9.10644105 + x = -14.893556509 + 9.10644105 Combine like terms: -9.10644105 + 9.10644105 = 0.00000000 0.00000000 + x = -14.893556509 + 9.10644105 x = -14.893556509 + 9.10644105 Combine like terms: -14.893556509 + 9.10644105 = -5.787115459 x = -5.787115459 Simplifying x = -5.787115459Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.999997559, -5.787115459}
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