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Simplifying -1x2 + 8x = -41 Reorder the terms: 8x + -1x2 = -41 Solving 8x + -1x2 = -41 Solving for variable 'x'. Reorder the terms: 41 + 8x + -1x2 = -41 + 41 Combine like terms: -41 + 41 = 0 41 + 8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -41 + -8x + x2 = 0 Move the constant term to the right: Add '41' to each side of the equation. -41 + -8x + 41 + x2 = 0 + 41 Reorder the terms: -41 + 41 + -8x + x2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -8x + x2 = 0 + 41 -8x + x2 = 0 + 41 Combine like terms: 0 + 41 = 41 -8x + x2 = 41 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 = 41 + 16 Reorder the terms: 16 + -8x + x2 = 41 + 16 Combine like terms: 41 + 16 = 57 16 + -8x + x2 = 57 Factor a perfect square on the left side: (x + -4)(x + -4) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (x + -4) equal to 7.549834435 and -7.549834435.Subproblem 1
x + -4 = 7.549834435 Simplifying x + -4 = 7.549834435 Reorder the terms: -4 + x = 7.549834435 Solving -4 + x = 7.549834435 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 = 7.549834435 + 4 Combine like terms: -4 + 4 = 0 0 + x = 7.549834435 + 4 x = 7.549834435 + 4 Combine like terms: 7.549834435 + 4 = 11.549834435 x = 11.549834435 Simplifying x = 11.549834435Subproblem 2
x + -4 = -7.549834435 Simplifying x + -4 = -7.549834435 Reorder the terms: -4 + x = -7.549834435 Solving -4 + x = -7.549834435 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 = -7.549834435 + 4 Combine like terms: -4 + 4 = 0 0 + x = -7.549834435 + 4 x = -7.549834435 + 4 Combine like terms: -7.549834435 + 4 = -3.549834435 x = -3.549834435 Simplifying x = -3.549834435Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.549834435, -3.549834435}
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