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Simplifying 8x2 + x + -660 = 0 Reorder the terms: -660 + x + 8x2 = 0 Solving -660 + x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -82.5 + 0.125x + x2 = 0 Move the constant term to the right: Add '82.5' to each side of the equation. -82.5 + 0.125x + 82.5 + x2 = 0 + 82.5 Reorder the terms: -82.5 + 82.5 + 0.125x + x2 = 0 + 82.5 Combine like terms: -82.5 + 82.5 = 0.0 0.0 + 0.125x + x2 = 0 + 82.5 0.125x + x2 = 0 + 82.5 Combine like terms: 0 + 82.5 = 82.5 0.125x + x2 = 82.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.125x + 0.25 + x2 = 82.5 + 0.25 Reorder the terms: 0.25 + 0.125x + x2 = 82.5 + 0.25 Combine like terms: 82.5 + 0.25 = 82.75 0.25 + 0.125x + x2 = 82.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 82.75 Calculate the square root of the right side: 9.096702699 Break this problem into two subproblems by setting (x + 0.5) equal to 9.096702699 and -9.096702699.Subproblem 1
x + 0.5 = 9.096702699 Simplifying x + 0.5 = 9.096702699 Reorder the terms: 0.5 + x = 9.096702699 Solving 0.5 + x = 9.096702699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 9.096702699 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 9.096702699 + -0.5 x = 9.096702699 + -0.5 Combine like terms: 9.096702699 + -0.5 = 8.596702699 x = 8.596702699 Simplifying x = 8.596702699Subproblem 2
x + 0.5 = -9.096702699 Simplifying x + 0.5 = -9.096702699 Reorder the terms: 0.5 + x = -9.096702699 Solving 0.5 + x = -9.096702699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -9.096702699 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -9.096702699 + -0.5 x = -9.096702699 + -0.5 Combine like terms: -9.096702699 + -0.5 = -9.596702699 x = -9.596702699 Simplifying x = -9.596702699Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.596702699, -9.596702699}
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