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Simplifying x2 + -36x + 72 = 0 Reorder the terms: 72 + -36x + x2 = 0 Solving 72 + -36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-72' to each side of the equation. 72 + -36x + -72 + x2 = 0 + -72 Reorder the terms: 72 + -72 + -36x + x2 = 0 + -72 Combine like terms: 72 + -72 = 0 0 + -36x + x2 = 0 + -72 -36x + x2 = 0 + -72 Combine like terms: 0 + -72 = -72 -36x + x2 = -72 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 = -72 + 324 Reorder the terms: 324 + -36x + x2 = -72 + 324 Combine like terms: -72 + 324 = 252 324 + -36x + x2 = 252 Factor a perfect square on the left side: (x + -18)(x + -18) = 252 Calculate the square root of the right side: 15.874507866 Break this problem into two subproblems by setting (x + -18) equal to 15.874507866 and -15.874507866.Subproblem 1
x + -18 = 15.874507866 Simplifying x + -18 = 15.874507866 Reorder the terms: -18 + x = 15.874507866 Solving -18 + x = 15.874507866 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 = 15.874507866 + 18 Combine like terms: -18 + 18 = 0 0 + x = 15.874507866 + 18 x = 15.874507866 + 18 Combine like terms: 15.874507866 + 18 = 33.874507866 x = 33.874507866 Simplifying x = 33.874507866Subproblem 2
x + -18 = -15.874507866 Simplifying x + -18 = -15.874507866 Reorder the terms: -18 + x = -15.874507866 Solving -18 + x = -15.874507866 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 = -15.874507866 + 18 Combine like terms: -18 + 18 = 0 0 + x = -15.874507866 + 18 x = -15.874507866 + 18 Combine like terms: -15.874507866 + 18 = 2.125492134 x = 2.125492134 Simplifying x = 2.125492134Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.874507866, 2.125492134}
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