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Simplifying x2 + 36x + 36 = 9 Reorder the terms: 36 + 36x + x2 = 9 Solving 36 + 36x + x2 = 9 Solving for variable 'x'. Reorder the terms: 36 + -9 + 36x + x2 = 9 + -9 Combine like terms: 36 + -9 = 27 27 + 36x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 27 + 36x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + 36x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + 36x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 36x + x2 = 0 + -27 36x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 36x + x2 = -27 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 = -27 + 324 Reorder the terms: 324 + 36x + x2 = -27 + 324 Combine like terms: -27 + 324 = 297 324 + 36x + x2 = 297 Factor a perfect square on the left side: (x + 18)(x + 18) = 297 Calculate the square root of the right side: 17.23368794 Break this problem into two subproblems by setting (x + 18) equal to 17.23368794 and -17.23368794.Subproblem 1
x + 18 = 17.23368794 Simplifying x + 18 = 17.23368794 Reorder the terms: 18 + x = 17.23368794 Solving 18 + x = 17.23368794 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 = 17.23368794 + -18 Combine like terms: 18 + -18 = 0 0 + x = 17.23368794 + -18 x = 17.23368794 + -18 Combine like terms: 17.23368794 + -18 = -0.76631206 x = -0.76631206 Simplifying x = -0.76631206Subproblem 2
x + 18 = -17.23368794 Simplifying x + 18 = -17.23368794 Reorder the terms: 18 + x = -17.23368794 Solving 18 + x = -17.23368794 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 = -17.23368794 + -18 Combine like terms: 18 + -18 = 0 0 + x = -17.23368794 + -18 x = -17.23368794 + -18 Combine like terms: -17.23368794 + -18 = -35.23368794 x = -35.23368794 Simplifying x = -35.23368794Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.76631206, -35.23368794}
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