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Simplifying x2 + 1 + 3x + 6 + x = 180 Reorder the terms: 1 + 6 + 3x + x + x2 = 180 Combine like terms: 1 + 6 = 7 7 + 3x + x + x2 = 180 Combine like terms: 3x + x = 4x 7 + 4x + x2 = 180 Solving 7 + 4x + x2 = 180 Solving for variable 'x'. Reorder the terms: 7 + -180 + 4x + x2 = 180 + -180 Combine like terms: 7 + -180 = -173 -173 + 4x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -173 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '173' to each side of the equation. -173 + 4x + 173 + x2 = 0 + 173 Reorder the terms: -173 + 173 + 4x + x2 = 0 + 173 Combine like terms: -173 + 173 = 0 0 + 4x + x2 = 0 + 173 4x + x2 = 0 + 173 Combine like terms: 0 + 173 = 173 4x + x2 = 173 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 173 + 4 Reorder the terms: 4 + 4x + x2 = 173 + 4 Combine like terms: 173 + 4 = 177 4 + 4x + x2 = 177 Factor a perfect square on the left side: (x + 2)(x + 2) = 177 Calculate the square root of the right side: 13.304134696 Break this problem into two subproblems by setting (x + 2) equal to 13.304134696 and -13.304134696.Subproblem 1
x + 2 = 13.304134696 Simplifying x + 2 = 13.304134696 Reorder the terms: 2 + x = 13.304134696 Solving 2 + x = 13.304134696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 13.304134696 + -2 Combine like terms: 2 + -2 = 0 0 + x = 13.304134696 + -2 x = 13.304134696 + -2 Combine like terms: 13.304134696 + -2 = 11.304134696 x = 11.304134696 Simplifying x = 11.304134696Subproblem 2
x + 2 = -13.304134696 Simplifying x + 2 = -13.304134696 Reorder the terms: 2 + x = -13.304134696 Solving 2 + x = -13.304134696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -13.304134696 + -2 Combine like terms: 2 + -2 = 0 0 + x = -13.304134696 + -2 x = -13.304134696 + -2 Combine like terms: -13.304134696 + -2 = -15.304134696 x = -15.304134696 Simplifying x = -15.304134696Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.304134696, -15.304134696}
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