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Simplifying x2 + -36x + 18 = 0 Reorder the terms: 18 + -36x + x2 = 0 Solving 18 + -36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -36x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + -36x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -36x + x2 = 0 + -18 -36x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 -36x + x2 = -18 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 = -18 + 324 Reorder the terms: 324 + -36x + x2 = -18 + 324 Combine like terms: -18 + 324 = 306 324 + -36x + x2 = 306 Factor a perfect square on the left side: (x + -18)(x + -18) = 306 Calculate the square root of the right side: 17.492855685 Break this problem into two subproblems by setting (x + -18) equal to 17.492855685 and -17.492855685.Subproblem 1
x + -18 = 17.492855685 Simplifying x + -18 = 17.492855685 Reorder the terms: -18 + x = 17.492855685 Solving -18 + x = 17.492855685 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 = 17.492855685 + 18 Combine like terms: -18 + 18 = 0 0 + x = 17.492855685 + 18 x = 17.492855685 + 18 Combine like terms: 17.492855685 + 18 = 35.492855685 x = 35.492855685 Simplifying x = 35.492855685Subproblem 2
x + -18 = -17.492855685 Simplifying x + -18 = -17.492855685 Reorder the terms: -18 + x = -17.492855685 Solving -18 + x = -17.492855685 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 = -17.492855685 + 18 Combine like terms: -18 + 18 = 0 0 + x = -17.492855685 + 18 x = -17.492855685 + 18 Combine like terms: -17.492855685 + 18 = 0.507144315 x = 0.507144315 Simplifying x = 0.507144315Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.492855685, 0.507144315}
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