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Simplifying x4 + -36x2 + 64 = 0 Reorder the terms: 64 + -36x2 + x4 = 0 Solving 64 + -36x2 + x4 = 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 + -36x2 + -64 + x4 = 0 + -64 Reorder the terms: 64 + -64 + -36x2 + x4 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + -36x2 + x4 = 0 + -64 -36x2 + x4 = 0 + -64 Combine like terms: 0 + -64 = -64 -36x2 + x4 = -64 The x term is -36x2. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36x2 + 324 + x4 = -64 + 324 Reorder the terms: 324 + -36x2 + x4 = -64 + 324 Combine like terms: -64 + 324 = 260 324 + -36x2 + x4 = 260 Factor a perfect square on the left side: (x2 + -18)(x2 + -18) = 260 Calculate the square root of the right side: 16.124515497 Break this problem into two subproblems by setting (x2 + -18) equal to 16.124515497 and -16.124515497.Subproblem 1
x2 + -18 = 16.124515497 Simplifying x2 + -18 = 16.124515497 Reorder the terms: -18 + x2 = 16.124515497 Solving -18 + x2 = 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 + x2 = 16.124515497 + 18 Combine like terms: -18 + 18 = 0 0 + x2 = 16.124515497 + 18 x2 = 16.124515497 + 18 Combine like terms: 16.124515497 + 18 = 34.124515497 x2 = 34.124515497 Simplifying x2 = 34.124515497 Take the square root of each side: x = {-5.841619253, 5.841619253}Subproblem 2
x2 + -18 = -16.124515497 Simplifying x2 + -18 = -16.124515497 Reorder the terms: -18 + x2 = -16.124515497 Solving -18 + x2 = -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 + x2 = -16.124515497 + 18 Combine like terms: -18 + 18 = 0 0 + x2 = -16.124515497 + 18 x2 = -16.124515497 + 18 Combine like terms: -16.124515497 + 18 = 1.875484503 x2 = 1.875484503 Simplifying x2 = 1.875484503 Take the square root of each side: x = {-1.369483298, 1.369483298}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.841619253, 5.841619253, -1.369483298, 1.369483298}
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