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Simplifying x2 + 36x + -9 = 0 Reorder the terms: -9 + 36x + x2 = 0 Solving -9 + 36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 36x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 36x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 36x + x2 = 0 + 9 36x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 36x + x2 = 9 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 = 9 + 324 Reorder the terms: 324 + 36x + x2 = 9 + 324 Combine like terms: 9 + 324 = 333 324 + 36x + x2 = 333 Factor a perfect square on the left side: (x + 18)(x + 18) = 333 Calculate the square root of the right side: 18.248287591 Break this problem into two subproblems by setting (x + 18) equal to 18.248287591 and -18.248287591.Subproblem 1
x + 18 = 18.248287591 Simplifying x + 18 = 18.248287591 Reorder the terms: 18 + x = 18.248287591 Solving 18 + x = 18.248287591 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 = 18.248287591 + -18 Combine like terms: 18 + -18 = 0 0 + x = 18.248287591 + -18 x = 18.248287591 + -18 Combine like terms: 18.248287591 + -18 = 0.248287591 x = 0.248287591 Simplifying x = 0.248287591Subproblem 2
x + 18 = -18.248287591 Simplifying x + 18 = -18.248287591 Reorder the terms: 18 + x = -18.248287591 Solving 18 + x = -18.248287591 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 = -18.248287591 + -18 Combine like terms: 18 + -18 = 0 0 + x = -18.248287591 + -18 x = -18.248287591 + -18 Combine like terms: -18.248287591 + -18 = -36.248287591 x = -36.248287591 Simplifying x = -36.248287591Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.248287591, -36.248287591}
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