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Simplifying x2 + 36x + -324 = -150 Reorder the terms: -324 + 36x + x2 = -150 Solving -324 + 36x + x2 = -150 Solving for variable 'x'. Reorder the terms: -324 + 150 + 36x + x2 = -150 + 150 Combine like terms: -324 + 150 = -174 -174 + 36x + x2 = -150 + 150 Combine like terms: -150 + 150 = 0 -174 + 36x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '174' to each side of the equation. -174 + 36x + 174 + x2 = 0 + 174 Reorder the terms: -174 + 174 + 36x + x2 = 0 + 174 Combine like terms: -174 + 174 = 0 0 + 36x + x2 = 0 + 174 36x + x2 = 0 + 174 Combine like terms: 0 + 174 = 174 36x + x2 = 174 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 = 174 + 324 Reorder the terms: 324 + 36x + x2 = 174 + 324 Combine like terms: 174 + 324 = 498 324 + 36x + x2 = 498 Factor a perfect square on the left side: (x + 18)(x + 18) = 498 Calculate the square root of the right side: 22.315913604 Break this problem into two subproblems by setting (x + 18) equal to 22.315913604 and -22.315913604.Subproblem 1
x + 18 = 22.315913604 Simplifying x + 18 = 22.315913604 Reorder the terms: 18 + x = 22.315913604 Solving 18 + x = 22.315913604 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 = 22.315913604 + -18 Combine like terms: 18 + -18 = 0 0 + x = 22.315913604 + -18 x = 22.315913604 + -18 Combine like terms: 22.315913604 + -18 = 4.315913604 x = 4.315913604 Simplifying x = 4.315913604Subproblem 2
x + 18 = -22.315913604 Simplifying x + 18 = -22.315913604 Reorder the terms: 18 + x = -22.315913604 Solving 18 + x = -22.315913604 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 = -22.315913604 + -18 Combine like terms: 18 + -18 = 0 0 + x = -22.315913604 + -18 x = -22.315913604 + -18 Combine like terms: -22.315913604 + -18 = -40.315913604 x = -40.315913604 Simplifying x = -40.315913604Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.315913604, -40.315913604}
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