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Simplifying 180 = x2 + 2x + 6 Reorder the terms: 180 = 6 + 2x + x2 Solving 180 = 6 + 2x + x2 Solving for variable 'x'. Combine like terms: 180 + -6 = 174 174 + -2x + -1x2 = 6 + 2x + x2 + -6 + -2x + -1x2 Reorder the terms: 174 + -2x + -1x2 = 6 + -6 + 2x + -2x + x2 + -1x2 Combine like terms: 6 + -6 = 0 174 + -2x + -1x2 = 0 + 2x + -2x + x2 + -1x2 174 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 174 + -2x + -1x2 = 0 + x2 + -1x2 174 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 174 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -174 + 2x + x2 = 0 Move the constant term to the right: Add '174' to each side of the equation. -174 + 2x + 174 + x2 = 0 + 174 Reorder the terms: -174 + 174 + 2x + x2 = 0 + 174 Combine like terms: -174 + 174 = 0 0 + 2x + x2 = 0 + 174 2x + x2 = 0 + 174 Combine like terms: 0 + 174 = 174 2x + x2 = 174 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 174 + 1 Reorder the terms: 1 + 2x + x2 = 174 + 1 Combine like terms: 174 + 1 = 175 1 + 2x + x2 = 175 Factor a perfect square on the left side: (x + 1)(x + 1) = 175 Calculate the square root of the right side: 13.228756555 Break this problem into two subproblems by setting (x + 1) equal to 13.228756555 and -13.228756555.Subproblem 1
x + 1 = 13.228756555 Simplifying x + 1 = 13.228756555 Reorder the terms: 1 + x = 13.228756555 Solving 1 + x = 13.228756555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 13.228756555 + -1 Combine like terms: 1 + -1 = 0 0 + x = 13.228756555 + -1 x = 13.228756555 + -1 Combine like terms: 13.228756555 + -1 = 12.228756555 x = 12.228756555 Simplifying x = 12.228756555Subproblem 2
x + 1 = -13.228756555 Simplifying x + 1 = -13.228756555 Reorder the terms: 1 + x = -13.228756555 Solving 1 + x = -13.228756555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -13.228756555 + -1 Combine like terms: 1 + -1 = 0 0 + x = -13.228756555 + -1 x = -13.228756555 + -1 Combine like terms: -13.228756555 + -1 = -14.228756555 x = -14.228756555 Simplifying x = -14.228756555Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.228756555, -14.228756555}
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