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Simplifying 81x2 + 7x + -56 = 0 Reorder the terms: -56 + 7x + 81x2 = 0 Solving -56 + 7x + 81x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. -0.6913580247 + 0.08641975309x + x2 = 0 Move the constant term to the right: Add '0.6913580247' to each side of the equation. -0.6913580247 + 0.08641975309x + 0.6913580247 + x2 = 0 + 0.6913580247 Reorder the terms: -0.6913580247 + 0.6913580247 + 0.08641975309x + x2 = 0 + 0.6913580247 Combine like terms: -0.6913580247 + 0.6913580247 = 0.0000000000 0.0000000000 + 0.08641975309x + x2 = 0 + 0.6913580247 0.08641975309x + x2 = 0 + 0.6913580247 Combine like terms: 0 + 0.6913580247 = 0.6913580247 0.08641975309x + x2 = 0.6913580247 The x term is 0.08641975309x. Take half its coefficient (0.04320987655). Square it (0.001867093431) and add it to both sides. Add '0.001867093431' to each side of the equation. 0.08641975309x + 0.001867093431 + x2 = 0.6913580247 + 0.001867093431 Reorder the terms: 0.001867093431 + 0.08641975309x + x2 = 0.6913580247 + 0.001867093431 Combine like terms: 0.6913580247 + 0.001867093431 = 0.693225118131 0.001867093431 + 0.08641975309x + x2 = 0.693225118131 Factor a perfect square on the left side: (x + 0.04320987655)(x + 0.04320987655) = 0.693225118131 Calculate the square root of the right side: 0.832601416 Break this problem into two subproblems by setting (x + 0.04320987655) equal to 0.832601416 and -0.832601416.Subproblem 1
x + 0.04320987655 = 0.832601416 Simplifying x + 0.04320987655 = 0.832601416 Reorder the terms: 0.04320987655 + x = 0.832601416 Solving 0.04320987655 + x = 0.832601416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04320987655' to each side of the equation. 0.04320987655 + -0.04320987655 + x = 0.832601416 + -0.04320987655 Combine like terms: 0.04320987655 + -0.04320987655 = 0.00000000000 0.00000000000 + x = 0.832601416 + -0.04320987655 x = 0.832601416 + -0.04320987655 Combine like terms: 0.832601416 + -0.04320987655 = 0.78939153945 x = 0.78939153945 Simplifying x = 0.78939153945Subproblem 2
x + 0.04320987655 = -0.832601416 Simplifying x + 0.04320987655 = -0.832601416 Reorder the terms: 0.04320987655 + x = -0.832601416 Solving 0.04320987655 + x = -0.832601416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04320987655' to each side of the equation. 0.04320987655 + -0.04320987655 + x = -0.832601416 + -0.04320987655 Combine like terms: 0.04320987655 + -0.04320987655 = 0.00000000000 0.00000000000 + x = -0.832601416 + -0.04320987655 x = -0.832601416 + -0.04320987655 Combine like terms: -0.832601416 + -0.04320987655 = -0.87581129255 x = -0.87581129255 Simplifying x = -0.87581129255Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.78939153945, -0.87581129255}
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