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Simplifying x2 + 36x + 150 = 0 Reorder the terms: 150 + 36x + x2 = 0 Solving 150 + 36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-150' to each side of the equation. 150 + 36x + -150 + x2 = 0 + -150 Reorder the terms: 150 + -150 + 36x + x2 = 0 + -150 Combine like terms: 150 + -150 = 0 0 + 36x + x2 = 0 + -150 36x + x2 = 0 + -150 Combine like terms: 0 + -150 = -150 36x + x2 = -150 The x term is 36x. Take half its coefficient (18). Square it (324) and add it to both sides. Add '324' to each side of the equation. 36x + 324 + x2 = -150 + 324 Reorder the terms: 324 + 36x + x2 = -150 + 324 Combine like terms: -150 + 324 = 174 324 + 36x + x2 = 174 Factor a perfect square on the left side: (x + 18)(x + 18) = 174 Calculate the square root of the right side: 13.190905958 Break this problem into two subproblems by setting (x + 18) equal to 13.190905958 and -13.190905958.Subproblem 1
x + 18 = 13.190905958 Simplifying x + 18 = 13.190905958 Reorder the terms: 18 + x = 13.190905958 Solving 18 + x = 13.190905958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = 13.190905958 + -18 Combine like terms: 18 + -18 = 0 0 + x = 13.190905958 + -18 x = 13.190905958 + -18 Combine like terms: 13.190905958 + -18 = -4.809094042 x = -4.809094042 Simplifying x = -4.809094042Subproblem 2
x + 18 = -13.190905958 Simplifying x + 18 = -13.190905958 Reorder the terms: 18 + x = -13.190905958 Solving 18 + x = -13.190905958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = -13.190905958 + -18 Combine like terms: 18 + -18 = 0 0 + x = -13.190905958 + -18 x = -13.190905958 + -18 Combine like terms: -13.190905958 + -18 = -31.190905958 x = -31.190905958 Simplifying x = -31.190905958Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.809094042, -31.190905958}
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