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Simplifying 0 = x2 + 8x + -186 Reorder the terms: 0 = -186 + 8x + x2 Solving 0 = -186 + 8x + x2 Solving for variable 'x'. Combine like terms: 0 + 186 = 186 186 + -8x + -1x2 = -186 + 8x + x2 + 186 + -8x + -1x2 Reorder the terms: 186 + -8x + -1x2 = -186 + 186 + 8x + -8x + x2 + -1x2 Combine like terms: -186 + 186 = 0 186 + -8x + -1x2 = 0 + 8x + -8x + x2 + -1x2 186 + -8x + -1x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 186 + -8x + -1x2 = 0 + x2 + -1x2 186 + -8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 186 + -8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -186 + 8x + x2 = 0 Move the constant term to the right: Add '186' to each side of the equation. -186 + 8x + 186 + x2 = 0 + 186 Reorder the terms: -186 + 186 + 8x + x2 = 0 + 186 Combine like terms: -186 + 186 = 0 0 + 8x + x2 = 0 + 186 8x + x2 = 0 + 186 Combine like terms: 0 + 186 = 186 8x + x2 = 186 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 = 186 + 16 Reorder the terms: 16 + 8x + x2 = 186 + 16 Combine like terms: 186 + 16 = 202 16 + 8x + x2 = 202 Factor a perfect square on the left side: (x + 4)(x + 4) = 202 Calculate the square root of the right side: 14.212670404 Break this problem into two subproblems by setting (x + 4) equal to 14.212670404 and -14.212670404.Subproblem 1
x + 4 = 14.212670404 Simplifying x + 4 = 14.212670404 Reorder the terms: 4 + x = 14.212670404 Solving 4 + x = 14.212670404 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 = 14.212670404 + -4 Combine like terms: 4 + -4 = 0 0 + x = 14.212670404 + -4 x = 14.212670404 + -4 Combine like terms: 14.212670404 + -4 = 10.212670404 x = 10.212670404 Simplifying x = 10.212670404Subproblem 2
x + 4 = -14.212670404 Simplifying x + 4 = -14.212670404 Reorder the terms: 4 + x = -14.212670404 Solving 4 + x = -14.212670404 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 = -14.212670404 + -4 Combine like terms: 4 + -4 = 0 0 + x = -14.212670404 + -4 x = -14.212670404 + -4 Combine like terms: -14.212670404 + -4 = -18.212670404 x = -18.212670404 Simplifying x = -18.212670404Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.212670404, -18.212670404}
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