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Simplifying -0.33x2 + 39.52x + -826.03 = 0 Reorder the terms: -826.03 + 39.52x + -0.33x2 = 0 Solving -826.03 + 39.52x + -0.33x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.33 the coefficient of the squared term: Divide each side by '-0.33'. 2503.121212 + -119.7575758x + x2 = 0 Move the constant term to the right: Add '-2503.121212' to each side of the equation. 2503.121212 + -119.7575758x + -2503.121212 + x2 = 0 + -2503.121212 Reorder the terms: 2503.121212 + -2503.121212 + -119.7575758x + x2 = 0 + -2503.121212 Combine like terms: 2503.121212 + -2503.121212 = 0.000000 0.000000 + -119.7575758x + x2 = 0 + -2503.121212 -119.7575758x + x2 = 0 + -2503.121212 Combine like terms: 0 + -2503.121212 = -2503.121212 -119.7575758x + x2 = -2503.121212 The x term is -119.7575758x. Take half its coefficient (-59.8787879). Square it (3585.469240) and add it to both sides. Add '3585.469240' to each side of the equation. -119.7575758x + 3585.469240 + x2 = -2503.121212 + 3585.469240 Reorder the terms: 3585.469240 + -119.7575758x + x2 = -2503.121212 + 3585.469240 Combine like terms: -2503.121212 + 3585.469240 = 1082.348028 3585.469240 + -119.7575758x + x2 = 1082.348028 Factor a perfect square on the left side: (x + -59.8787879)(x + -59.8787879) = 1082.348028 Calculate the square root of the right side: 32.899058163 Break this problem into two subproblems by setting (x + -59.8787879) equal to 32.899058163 and -32.899058163.Subproblem 1
x + -59.8787879 = 32.899058163 Simplifying x + -59.8787879 = 32.899058163 Reorder the terms: -59.8787879 + x = 32.899058163 Solving -59.8787879 + x = 32.899058163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '59.8787879' to each side of the equation. -59.8787879 + 59.8787879 + x = 32.899058163 + 59.8787879 Combine like terms: -59.8787879 + 59.8787879 = 0.0000000 0.0000000 + x = 32.899058163 + 59.8787879 x = 32.899058163 + 59.8787879 Combine like terms: 32.899058163 + 59.8787879 = 92.777846063 x = 92.777846063 Simplifying x = 92.777846063Subproblem 2
x + -59.8787879 = -32.899058163 Simplifying x + -59.8787879 = -32.899058163 Reorder the terms: -59.8787879 + x = -32.899058163 Solving -59.8787879 + x = -32.899058163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '59.8787879' to each side of the equation. -59.8787879 + 59.8787879 + x = -32.899058163 + 59.8787879 Combine like terms: -59.8787879 + 59.8787879 = 0.0000000 0.0000000 + x = -32.899058163 + 59.8787879 x = -32.899058163 + 59.8787879 Combine like terms: -32.899058163 + 59.8787879 = 26.979729737 x = 26.979729737 Simplifying x = 26.979729737Solution
The solution to the problem is based on the solutions from the subproblems. x = {92.777846063, 26.979729737}
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