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Simplifying 0 = x2 + -8x + -80 Reorder the terms: 0 = -80 + -8x + x2 Solving 0 = -80 + -8x + x2 Solving for variable 'x'. Combine like terms: 0 + 80 = 80 80 + 8x + -1x2 = -80 + -8x + x2 + 80 + 8x + -1x2 Reorder the terms: 80 + 8x + -1x2 = -80 + 80 + -8x + 8x + x2 + -1x2 Combine like terms: -80 + 80 = 0 80 + 8x + -1x2 = 0 + -8x + 8x + x2 + -1x2 80 + 8x + -1x2 = -8x + 8x + x2 + -1x2 Combine like terms: -8x + 8x = 0 80 + 8x + -1x2 = 0 + x2 + -1x2 80 + 8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 80 + 8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -80 + -8x + x2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + -8x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + -8x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -8x + x2 = 0 + 80 -8x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 -8x + x2 = 80 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 = 80 + 16 Reorder the terms: 16 + -8x + x2 = 80 + 16 Combine like terms: 80 + 16 = 96 16 + -8x + x2 = 96 Factor a perfect square on the left side: (x + -4)(x + -4) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (x + -4) equal to 9.797958971 and -9.797958971.Subproblem 1
x + -4 = 9.797958971 Simplifying x + -4 = 9.797958971 Reorder the terms: -4 + x = 9.797958971 Solving -4 + x = 9.797958971 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 = 9.797958971 + 4 Combine like terms: -4 + 4 = 0 0 + x = 9.797958971 + 4 x = 9.797958971 + 4 Combine like terms: 9.797958971 + 4 = 13.797958971 x = 13.797958971 Simplifying x = 13.797958971Subproblem 2
x + -4 = -9.797958971 Simplifying x + -4 = -9.797958971 Reorder the terms: -4 + x = -9.797958971 Solving -4 + x = -9.797958971 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 = -9.797958971 + 4 Combine like terms: -4 + 4 = 0 0 + x = -9.797958971 + 4 x = -9.797958971 + 4 Combine like terms: -9.797958971 + 4 = -5.797958971 x = -5.797958971 Simplifying x = -5.797958971Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.797958971, -5.797958971}
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