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Simplifying x4 + -36x2 + 21.7 = 0 Reorder the terms: 21.7 + -36x2 + x4 = 0 Solving 21.7 + -36x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-21.7' to each side of the equation. 21.7 + -36x2 + -21.7 + x4 = 0 + -21.7 Reorder the terms: 21.7 + -21.7 + -36x2 + x4 = 0 + -21.7 Combine like terms: 21.7 + -21.7 = 0.0 0.0 + -36x2 + x4 = 0 + -21.7 -36x2 + x4 = 0 + -21.7 Combine like terms: 0 + -21.7 = -21.7 -36x2 + x4 = -21.7 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 = -21.7 + 324 Reorder the terms: 324 + -36x2 + x4 = -21.7 + 324 Combine like terms: -21.7 + 324 = 302.3 324 + -36x2 + x4 = 302.3 Factor a perfect square on the left side: (x2 + -18)(x2 + -18) = 302.3 Calculate the square root of the right side: 17.386776585 Break this problem into two subproblems by setting (x2 + -18) equal to 17.386776585 and -17.386776585.Subproblem 1
x2 + -18 = 17.386776585 Simplifying x2 + -18 = 17.386776585 Reorder the terms: -18 + x2 = 17.386776585 Solving -18 + x2 = 17.386776585 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 = 17.386776585 + 18 Combine like terms: -18 + 18 = 0 0 + x2 = 17.386776585 + 18 x2 = 17.386776585 + 18 Combine like terms: 17.386776585 + 18 = 35.386776585 x2 = 35.386776585 Simplifying x2 = 35.386776585 Take the square root of each side: x = {-5.948678558, 5.948678558}Subproblem 2
x2 + -18 = -17.386776585 Simplifying x2 + -18 = -17.386776585 Reorder the terms: -18 + x2 = -17.386776585 Solving -18 + x2 = -17.386776585 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 = -17.386776585 + 18 Combine like terms: -18 + 18 = 0 0 + x2 = -17.386776585 + 18 x2 = -17.386776585 + 18 Combine like terms: -17.386776585 + 18 = 0.613223415 x2 = 0.613223415 Simplifying x2 = 0.613223415 Take the square root of each side: x = {-0.783085829, 0.783085829}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.948678558, 5.948678558, -0.783085829, 0.783085829}
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