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Simplifying 185 = x2 + 8x + 144 Reorder the terms: 185 = 144 + 8x + x2 Solving 185 = 144 + 8x + x2 Solving for variable 'x'. Combine like terms: 185 + -144 = 41 41 + -8x + -1x2 = 144 + 8x + x2 + -144 + -8x + -1x2 Reorder the terms: 41 + -8x + -1x2 = 144 + -144 + 8x + -8x + x2 + -1x2 Combine like terms: 144 + -144 = 0 41 + -8x + -1x2 = 0 + 8x + -8x + x2 + -1x2 41 + -8x + -1x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 41 + -8x + -1x2 = 0 + x2 + -1x2 41 + -8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 41 + -8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -41 + 8x + x2 = 0 Move the constant term to the right: Add '41' to each side of the equation. -41 + 8x + 41 + x2 = 0 + 41 Reorder the terms: -41 + 41 + 8x + x2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + 8x + x2 = 0 + 41 8x + x2 = 0 + 41 Combine like terms: 0 + 41 = 41 8x + x2 = 41 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 = 41 + 16 Reorder the terms: 16 + 8x + x2 = 41 + 16 Combine like terms: 41 + 16 = 57 16 + 8x + x2 = 57 Factor a perfect square on the left side: (x + 4)(x + 4) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (x + 4) equal to 7.549834435 and -7.549834435.Subproblem 1
x + 4 = 7.549834435 Simplifying x + 4 = 7.549834435 Reorder the terms: 4 + x = 7.549834435 Solving 4 + x = 7.549834435 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 = 7.549834435 + -4 Combine like terms: 4 + -4 = 0 0 + x = 7.549834435 + -4 x = 7.549834435 + -4 Combine like terms: 7.549834435 + -4 = 3.549834435 x = 3.549834435 Simplifying x = 3.549834435Subproblem 2
x + 4 = -7.549834435 Simplifying x + 4 = -7.549834435 Reorder the terms: 4 + x = -7.549834435 Solving 4 + x = -7.549834435 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 = -7.549834435 + -4 Combine like terms: 4 + -4 = 0 0 + x = -7.549834435 + -4 x = -7.549834435 + -4 Combine like terms: -7.549834435 + -4 = -11.549834435 x = -11.549834435 Simplifying x = -11.549834435Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.549834435, -11.549834435}
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