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Simplifying x2 + -36x + -0.5 = 0 Reorder the terms: -0.5 + -36x + x2 = 0 Solving -0.5 + -36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -36x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -36x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -36x + x2 = 0 + 0.5 -36x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -36x + x2 = 0.5 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 = 0.5 + 324 Reorder the terms: 324 + -36x + x2 = 0.5 + 324 Combine like terms: 0.5 + 324 = 324.5 324 + -36x + x2 = 324.5 Factor a perfect square on the left side: (x + -18)(x + -18) = 324.5 Calculate the square root of the right side: 18.013883535 Break this problem into two subproblems by setting (x + -18) equal to 18.013883535 and -18.013883535.Subproblem 1
x + -18 = 18.013883535 Simplifying x + -18 = 18.013883535 Reorder the terms: -18 + x = 18.013883535 Solving -18 + x = 18.013883535 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 = 18.013883535 + 18 Combine like terms: -18 + 18 = 0 0 + x = 18.013883535 + 18 x = 18.013883535 + 18 Combine like terms: 18.013883535 + 18 = 36.013883535 x = 36.013883535 Simplifying x = 36.013883535Subproblem 2
x + -18 = -18.013883535 Simplifying x + -18 = -18.013883535 Reorder the terms: -18 + x = -18.013883535 Solving -18 + x = -18.013883535 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 = -18.013883535 + 18 Combine like terms: -18 + 18 = 0 0 + x = -18.013883535 + 18 x = -18.013883535 + 18 Combine like terms: -18.013883535 + 18 = -0.013883535 x = -0.013883535 Simplifying x = -0.013883535Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.013883535, -0.013883535}
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