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Simplifying x2 + 6 = 36x Reorder the terms: 6 + x2 = 36x Solving 6 + x2 = 36x Solving for variable 'x'. Reorder the terms: 6 + -36x + x2 = 36x + -36x Combine like terms: 36x + -36x = 0 6 + -36x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -36x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -36x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -36x + x2 = 0 + -6 -36x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -36x + x2 = -6 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 = -6 + 324 Reorder the terms: 324 + -36x + x2 = -6 + 324 Combine like terms: -6 + 324 = 318 324 + -36x + x2 = 318 Factor a perfect square on the left side: (x + -18)(x + -18) = 318 Calculate the square root of the right side: 17.8325545 Break this problem into two subproblems by setting (x + -18) equal to 17.8325545 and -17.8325545.Subproblem 1
x + -18 = 17.8325545 Simplifying x + -18 = 17.8325545 Reorder the terms: -18 + x = 17.8325545 Solving -18 + x = 17.8325545 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 = 17.8325545 + 18 Combine like terms: -18 + 18 = 0 0 + x = 17.8325545 + 18 x = 17.8325545 + 18 Combine like terms: 17.8325545 + 18 = 35.8325545 x = 35.8325545 Simplifying x = 35.8325545Subproblem 2
x + -18 = -17.8325545 Simplifying x + -18 = -17.8325545 Reorder the terms: -18 + x = -17.8325545 Solving -18 + x = -17.8325545 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 = -17.8325545 + 18 Combine like terms: -18 + 18 = 0 0 + x = -17.8325545 + 18 x = -17.8325545 + 18 Combine like terms: -17.8325545 + 18 = 0.1674455 x = 0.1674455 Simplifying x = 0.1674455Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.8325545, 0.1674455}
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