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Simplifying x2 + 3x + 10 + x = 180 Reorder the terms: 10 + 3x + x + x2 = 180 Combine like terms: 3x + x = 4x 10 + 4x + x2 = 180 Solving 10 + 4x + x2 = 180 Solving for variable 'x'. Reorder the terms: 10 + -180 + 4x + x2 = 180 + -180 Combine like terms: 10 + -180 = -170 -170 + 4x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -170 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '170' to each side of the equation. -170 + 4x + 170 + x2 = 0 + 170 Reorder the terms: -170 + 170 + 4x + x2 = 0 + 170 Combine like terms: -170 + 170 = 0 0 + 4x + x2 = 0 + 170 4x + x2 = 0 + 170 Combine like terms: 0 + 170 = 170 4x + x2 = 170 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 = 170 + 4 Reorder the terms: 4 + 4x + x2 = 170 + 4 Combine like terms: 170 + 4 = 174 4 + 4x + x2 = 174 Factor a perfect square on the left side: (x + 2)(x + 2) = 174 Calculate the square root of the right side: 13.190905958 Break this problem into two subproblems by setting (x + 2) equal to 13.190905958 and -13.190905958.Subproblem 1
x + 2 = 13.190905958 Simplifying x + 2 = 13.190905958 Reorder the terms: 2 + x = 13.190905958 Solving 2 + x = 13.190905958 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 = 13.190905958 + -2 Combine like terms: 2 + -2 = 0 0 + x = 13.190905958 + -2 x = 13.190905958 + -2 Combine like terms: 13.190905958 + -2 = 11.190905958 x = 11.190905958 Simplifying x = 11.190905958Subproblem 2
x + 2 = -13.190905958 Simplifying x + 2 = -13.190905958 Reorder the terms: 2 + x = -13.190905958 Solving 2 + x = -13.190905958 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 = -13.190905958 + -2 Combine like terms: 2 + -2 = 0 0 + x = -13.190905958 + -2 x = -13.190905958 + -2 Combine like terms: -13.190905958 + -2 = -15.190905958 x = -15.190905958 Simplifying x = -15.190905958Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.190905958, -15.190905958}
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