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Simplifying x2 + -36x + 64 = 0 Reorder the terms: 64 + -36x + x2 = 0 Solving 64 + -36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-64' to each side of the equation. 64 + -36x + -64 + x2 = 0 + -64 Reorder the terms: 64 + -64 + -36x + x2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + -36x + x2 = 0 + -64 -36x + x2 = 0 + -64 Combine like terms: 0 + -64 = -64 -36x + x2 = -64 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 = -64 + 324 Reorder the terms: 324 + -36x + x2 = -64 + 324 Combine like terms: -64 + 324 = 260 324 + -36x + x2 = 260 Factor a perfect square on the left side: (x + -18)(x + -18) = 260 Calculate the square root of the right side: 16.124515497 Break this problem into two subproblems by setting (x + -18) equal to 16.124515497 and -16.124515497.Subproblem 1
x + -18 = 16.124515497 Simplifying x + -18 = 16.124515497 Reorder the terms: -18 + x = 16.124515497 Solving -18 + x = 16.124515497 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 = 16.124515497 + 18 Combine like terms: -18 + 18 = 0 0 + x = 16.124515497 + 18 x = 16.124515497 + 18 Combine like terms: 16.124515497 + 18 = 34.124515497 x = 34.124515497 Simplifying x = 34.124515497Subproblem 2
x + -18 = -16.124515497 Simplifying x + -18 = -16.124515497 Reorder the terms: -18 + x = -16.124515497 Solving -18 + x = -16.124515497 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 = -16.124515497 + 18 Combine like terms: -18 + 18 = 0 0 + x = -16.124515497 + 18 x = -16.124515497 + 18 Combine like terms: -16.124515497 + 18 = 1.875484503 x = 1.875484503 Simplifying x = 1.875484503Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.124515497, 1.875484503}
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