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Simplifying -1x2 + 8x = -39.25 Reorder the terms: 8x + -1x2 = -39.25 Solving 8x + -1x2 = -39.25 Solving for variable 'x'. Reorder the terms: 39.25 + 8x + -1x2 = -39.25 + 39.25 Combine like terms: -39.25 + 39.25 = 0.00 39.25 + 8x + -1x2 = 0.00 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -39.25 + -8x + x2 = 0.00 Move the constant term to the right: Add '39.25' to each side of the equation. -39.25 + -8x + 39.25 + x2 = 0.00 + 39.25 Reorder the terms: -39.25 + 39.25 + -8x + x2 = 0.00 + 39.25 Combine like terms: -39.25 + 39.25 = 0.00 0.00 + -8x + x2 = 0.00 + 39.25 -8x + x2 = 0.00 + 39.25 Combine like terms: 0.00 + 39.25 = 39.25 -8x + x2 = 39.25 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 39.25 + 16 Reorder the terms: 16 + -8x + x2 = 39.25 + 16 Combine like terms: 39.25 + 16 = 55.25 16 + -8x + x2 = 55.25 Factor a perfect square on the left side: (x + -4)(x + -4) = 55.25 Calculate the square root of the right side: 7.433034374 Break this problem into two subproblems by setting (x + -4) equal to 7.433034374 and -7.433034374.Subproblem 1
x + -4 = 7.433034374 Simplifying x + -4 = 7.433034374 Reorder the terms: -4 + x = 7.433034374 Solving -4 + x = 7.433034374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 7.433034374 + 4 Combine like terms: -4 + 4 = 0 0 + x = 7.433034374 + 4 x = 7.433034374 + 4 Combine like terms: 7.433034374 + 4 = 11.433034374 x = 11.433034374 Simplifying x = 11.433034374Subproblem 2
x + -4 = -7.433034374 Simplifying x + -4 = -7.433034374 Reorder the terms: -4 + x = -7.433034374 Solving -4 + x = -7.433034374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -7.433034374 + 4 Combine like terms: -4 + 4 = 0 0 + x = -7.433034374 + 4 x = -7.433034374 + 4 Combine like terms: -7.433034374 + 4 = -3.433034374 x = -3.433034374 Simplifying x = -3.433034374Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.433034374, -3.433034374}
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