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Simplifying x4 + -36x2 + 32 = 0 Reorder the terms: 32 + -36x2 + x4 = 0 Solving 32 + -36x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + -36x2 + -32 + x4 = 0 + -32 Reorder the terms: 32 + -32 + -36x2 + x4 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -36x2 + x4 = 0 + -32 -36x2 + x4 = 0 + -32 Combine like terms: 0 + -32 = -32 -36x2 + x4 = -32 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 = -32 + 324 Reorder the terms: 324 + -36x2 + x4 = -32 + 324 Combine like terms: -32 + 324 = 292 324 + -36x2 + x4 = 292 Factor a perfect square on the left side: (x2 + -18)(x2 + -18) = 292 Calculate the square root of the right side: 17.088007491 Break this problem into two subproblems by setting (x2 + -18) equal to 17.088007491 and -17.088007491.Subproblem 1
x2 + -18 = 17.088007491 Simplifying x2 + -18 = 17.088007491 Reorder the terms: -18 + x2 = 17.088007491 Solving -18 + x2 = 17.088007491 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 = 17.088007491 + 18 Combine like terms: -18 + 18 = 0 0 + x2 = 17.088007491 + 18 x2 = 17.088007491 + 18 Combine like terms: 17.088007491 + 18 = 35.088007491 x2 = 35.088007491 Simplifying x2 = 35.088007491 Take the square root of each side: x = {-5.923513104, 5.923513104}Subproblem 2
x2 + -18 = -17.088007491 Simplifying x2 + -18 = -17.088007491 Reorder the terms: -18 + x2 = -17.088007491 Solving -18 + x2 = -17.088007491 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 = -17.088007491 + 18 Combine like terms: -18 + 18 = 0 0 + x2 = -17.088007491 + 18 x2 = -17.088007491 + 18 Combine like terms: -17.088007491 + 18 = 0.911992509 x2 = 0.911992509 Simplifying x2 = 0.911992509 Take the square root of each side: x = {-0.954982989, 0.954982989}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.923513104, 5.923513104, -0.954982989, 0.954982989}
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