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Simplifying 0 = x2 + 16x + -163 Reorder the terms: 0 = -163 + 16x + x2 Solving 0 = -163 + 16x + x2 Solving for variable 'x'. Combine like terms: 0 + 163 = 163 163 + -16x + -1x2 = -163 + 16x + x2 + 163 + -16x + -1x2 Reorder the terms: 163 + -16x + -1x2 = -163 + 163 + 16x + -16x + x2 + -1x2 Combine like terms: -163 + 163 = 0 163 + -16x + -1x2 = 0 + 16x + -16x + x2 + -1x2 163 + -16x + -1x2 = 16x + -16x + x2 + -1x2 Combine like terms: 16x + -16x = 0 163 + -16x + -1x2 = 0 + x2 + -1x2 163 + -16x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 163 + -16x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -163 + 16x + x2 = 0 Move the constant term to the right: Add '163' to each side of the equation. -163 + 16x + 163 + x2 = 0 + 163 Reorder the terms: -163 + 163 + 16x + x2 = 0 + 163 Combine like terms: -163 + 163 = 0 0 + 16x + x2 = 0 + 163 16x + x2 = 0 + 163 Combine like terms: 0 + 163 = 163 16x + x2 = 163 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 = 163 + 64 Reorder the terms: 64 + 16x + x2 = 163 + 64 Combine like terms: 163 + 64 = 227 64 + 16x + x2 = 227 Factor a perfect square on the left side: (x + 8)(x + 8) = 227 Calculate the square root of the right side: 15.066519173 Break this problem into two subproblems by setting (x + 8) equal to 15.066519173 and -15.066519173.Subproblem 1
x + 8 = 15.066519173 Simplifying x + 8 = 15.066519173 Reorder the terms: 8 + x = 15.066519173 Solving 8 + x = 15.066519173 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 = 15.066519173 + -8 Combine like terms: 8 + -8 = 0 0 + x = 15.066519173 + -8 x = 15.066519173 + -8 Combine like terms: 15.066519173 + -8 = 7.066519173 x = 7.066519173 Simplifying x = 7.066519173Subproblem 2
x + 8 = -15.066519173 Simplifying x + 8 = -15.066519173 Reorder the terms: 8 + x = -15.066519173 Solving 8 + x = -15.066519173 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 = -15.066519173 + -8 Combine like terms: 8 + -8 = 0 0 + x = -15.066519173 + -8 x = -15.066519173 + -8 Combine like terms: -15.066519173 + -8 = -23.066519173 x = -23.066519173 Simplifying x = -23.066519173Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.066519173, -23.066519173}
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