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Simplifying 8(x2 + -1) = 77x Reorder the terms: 8(-1 + x2) = 77x (-1 * 8 + x2 * 8) = 77x (-8 + 8x2) = 77x Solving -8 + 8x2 = 77x Solving for variable 'x'. Reorder the terms: -8 + -77x + 8x2 = 77x + -77x Combine like terms: 77x + -77x = 0 -8 + -77x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1 + -9.625x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -9.625x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -9.625x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -9.625x + x2 = 0 + 1 -9.625x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -9.625x + x2 = 1 The x term is -9.625x. Take half its coefficient (-4.8125). Square it (23.16015625) and add it to both sides. Add '23.16015625' to each side of the equation. -9.625x + 23.16015625 + x2 = 1 + 23.16015625 Reorder the terms: 23.16015625 + -9.625x + x2 = 1 + 23.16015625 Combine like terms: 1 + 23.16015625 = 24.16015625 23.16015625 + -9.625x + x2 = 24.16015625 Factor a perfect square on the left side: (x + -4.8125)(x + -4.8125) = 24.16015625 Calculate the square root of the right side: 4.915298185 Break this problem into two subproblems by setting (x + -4.8125) equal to 4.915298185 and -4.915298185.Subproblem 1
x + -4.8125 = 4.915298185 Simplifying x + -4.8125 = 4.915298185 Reorder the terms: -4.8125 + x = 4.915298185 Solving -4.8125 + x = 4.915298185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.8125' to each side of the equation. -4.8125 + 4.8125 + x = 4.915298185 + 4.8125 Combine like terms: -4.8125 + 4.8125 = 0.0000 0.0000 + x = 4.915298185 + 4.8125 x = 4.915298185 + 4.8125 Combine like terms: 4.915298185 + 4.8125 = 9.727798185 x = 9.727798185 Simplifying x = 9.727798185Subproblem 2
x + -4.8125 = -4.915298185 Simplifying x + -4.8125 = -4.915298185 Reorder the terms: -4.8125 + x = -4.915298185 Solving -4.8125 + x = -4.915298185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.8125' to each side of the equation. -4.8125 + 4.8125 + x = -4.915298185 + 4.8125 Combine like terms: -4.8125 + 4.8125 = 0.0000 0.0000 + x = -4.915298185 + 4.8125 x = -4.915298185 + 4.8125 Combine like terms: -4.915298185 + 4.8125 = -0.102798185 x = -0.102798185 Simplifying x = -0.102798185Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.727798185, -0.102798185}
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