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Simplifying -1x2 + -16x + 64 = 2 Reorder the terms: 64 + -16x + -1x2 = 2 Solving 64 + -16x + -1x2 = 2 Solving for variable 'x'. Reorder the terms: 64 + -2 + -16x + -1x2 = 2 + -2 Combine like terms: 64 + -2 = 62 62 + -16x + -1x2 = 2 + -2 Combine like terms: 2 + -2 = 0 62 + -16x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -62 + 16x + x2 = 0 Move the constant term to the right: Add '62' to each side of the equation. -62 + 16x + 62 + x2 = 0 + 62 Reorder the terms: -62 + 62 + 16x + x2 = 0 + 62 Combine like terms: -62 + 62 = 0 0 + 16x + x2 = 0 + 62 16x + x2 = 0 + 62 Combine like terms: 0 + 62 = 62 16x + x2 = 62 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 62 + 64 Reorder the terms: 64 + 16x + x2 = 62 + 64 Combine like terms: 62 + 64 = 126 64 + 16x + x2 = 126 Factor a perfect square on the left side: (x + 8)(x + 8) = 126 Calculate the square root of the right side: 11.22497216 Break this problem into two subproblems by setting (x + 8) equal to 11.22497216 and -11.22497216.Subproblem 1
x + 8 = 11.22497216 Simplifying x + 8 = 11.22497216 Reorder the terms: 8 + x = 11.22497216 Solving 8 + x = 11.22497216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 11.22497216 + -8 Combine like terms: 8 + -8 = 0 0 + x = 11.22497216 + -8 x = 11.22497216 + -8 Combine like terms: 11.22497216 + -8 = 3.22497216 x = 3.22497216 Simplifying x = 3.22497216Subproblem 2
x + 8 = -11.22497216 Simplifying x + 8 = -11.22497216 Reorder the terms: 8 + x = -11.22497216 Solving 8 + x = -11.22497216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -11.22497216 + -8 Combine like terms: 8 + -8 = 0 0 + x = -11.22497216 + -8 x = -11.22497216 + -8 Combine like terms: -11.22497216 + -8 = -19.22497216 x = -19.22497216 Simplifying x = -19.22497216Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.22497216, -19.22497216}
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