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Simplifying (8.2x + -3.5) * x = 84.6 Reorder the terms: (-3.5 + 8.2x) * x = 84.6 Reorder the terms for easier multiplication: x(-3.5 + 8.2x) = 84.6 (-3.5 * x + 8.2x * x) = 84.6 (-3.5x + 8.2x2) = 84.6 Solving -3.5x + 8.2x2 = 84.6 Solving for variable 'x'. Reorder the terms: -84.6 + -3.5x + 8.2x2 = 84.6 + -84.6 Combine like terms: 84.6 + -84.6 = 0.0 -84.6 + -3.5x + 8.2x2 = 0.0 Begin completing the square. Divide all terms by 8.2 the coefficient of the squared term: Divide each side by '8.2'. -10.31707317 + -0.4268292683x + x2 = 0 Move the constant term to the right: Add '10.31707317' to each side of the equation. -10.31707317 + -0.4268292683x + 10.31707317 + x2 = 0 + 10.31707317 Reorder the terms: -10.31707317 + 10.31707317 + -0.4268292683x + x2 = 0 + 10.31707317 Combine like terms: -10.31707317 + 10.31707317 = 0.00000000 0.00000000 + -0.4268292683x + x2 = 0 + 10.31707317 -0.4268292683x + x2 = 0 + 10.31707317 Combine like terms: 0 + 10.31707317 = 10.31707317 -0.4268292683x + x2 = 10.31707317 The x term is -0.4268292683x. Take half its coefficient (-0.2134146342). Square it (0.04554580609) and add it to both sides. Add '0.04554580609' to each side of the equation. -0.4268292683x + 0.04554580609 + x2 = 10.31707317 + 0.04554580609 Reorder the terms: 0.04554580609 + -0.4268292683x + x2 = 10.31707317 + 0.04554580609 Combine like terms: 10.31707317 + 0.04554580609 = 10.36261897609 0.04554580609 + -0.4268292683x + x2 = 10.36261897609 Factor a perfect square on the left side: (x + -0.2134146342)(x + -0.2134146342) = 10.36261897609 Calculate the square root of the right side: 3.2191022 Break this problem into two subproblems by setting (x + -0.2134146342) equal to 3.2191022 and -3.2191022.Subproblem 1
x + -0.2134146342 = 3.2191022 Simplifying x + -0.2134146342 = 3.2191022 Reorder the terms: -0.2134146342 + x = 3.2191022 Solving -0.2134146342 + x = 3.2191022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2134146342' to each side of the equation. -0.2134146342 + 0.2134146342 + x = 3.2191022 + 0.2134146342 Combine like terms: -0.2134146342 + 0.2134146342 = 0.0000000000 0.0000000000 + x = 3.2191022 + 0.2134146342 x = 3.2191022 + 0.2134146342 Combine like terms: 3.2191022 + 0.2134146342 = 3.4325168342 x = 3.4325168342 Simplifying x = 3.4325168342Subproblem 2
x + -0.2134146342 = -3.2191022 Simplifying x + -0.2134146342 = -3.2191022 Reorder the terms: -0.2134146342 + x = -3.2191022 Solving -0.2134146342 + x = -3.2191022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2134146342' to each side of the equation. -0.2134146342 + 0.2134146342 + x = -3.2191022 + 0.2134146342 Combine like terms: -0.2134146342 + 0.2134146342 = 0.0000000000 0.0000000000 + x = -3.2191022 + 0.2134146342 x = -3.2191022 + 0.2134146342 Combine like terms: -3.2191022 + 0.2134146342 = -3.0056875658 x = -3.0056875658 Simplifying x = -3.0056875658Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.4325168342, -3.0056875658}
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