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Simplifying 0 = x2 + 8x + -91 Reorder the terms: 0 = -91 + 8x + x2 Solving 0 = -91 + 8x + x2 Solving for variable 'x'. Combine like terms: 0 + 91 = 91 91 + -8x + -1x2 = -91 + 8x + x2 + 91 + -8x + -1x2 Reorder the terms: 91 + -8x + -1x2 = -91 + 91 + 8x + -8x + x2 + -1x2 Combine like terms: -91 + 91 = 0 91 + -8x + -1x2 = 0 + 8x + -8x + x2 + -1x2 91 + -8x + -1x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 91 + -8x + -1x2 = 0 + x2 + -1x2 91 + -8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 91 + -8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -91 + 8x + x2 = 0 Move the constant term to the right: Add '91' to each side of the equation. -91 + 8x + 91 + x2 = 0 + 91 Reorder the terms: -91 + 91 + 8x + x2 = 0 + 91 Combine like terms: -91 + 91 = 0 0 + 8x + x2 = 0 + 91 8x + x2 = 0 + 91 Combine like terms: 0 + 91 = 91 8x + x2 = 91 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 = 91 + 16 Reorder the terms: 16 + 8x + x2 = 91 + 16 Combine like terms: 91 + 16 = 107 16 + 8x + x2 = 107 Factor a perfect square on the left side: (x + 4)(x + 4) = 107 Calculate the square root of the right side: 10.344080433 Break this problem into two subproblems by setting (x + 4) equal to 10.344080433 and -10.344080433.Subproblem 1
x + 4 = 10.344080433 Simplifying x + 4 = 10.344080433 Reorder the terms: 4 + x = 10.344080433 Solving 4 + x = 10.344080433 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 = 10.344080433 + -4 Combine like terms: 4 + -4 = 0 0 + x = 10.344080433 + -4 x = 10.344080433 + -4 Combine like terms: 10.344080433 + -4 = 6.344080433 x = 6.344080433 Simplifying x = 6.344080433Subproblem 2
x + 4 = -10.344080433 Simplifying x + 4 = -10.344080433 Reorder the terms: 4 + x = -10.344080433 Solving 4 + x = -10.344080433 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 = -10.344080433 + -4 Combine like terms: 4 + -4 = 0 0 + x = -10.344080433 + -4 x = -10.344080433 + -4 Combine like terms: -10.344080433 + -4 = -14.344080433 x = -14.344080433 Simplifying x = -14.344080433Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.344080433, -14.344080433}
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