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Simplifying x4 + 10x2 + -150 = 0 Reorder the terms: -150 + 10x2 + x4 = 0 Solving -150 + 10x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '150' to each side of the equation. -150 + 10x2 + 150 + x4 = 0 + 150 Reorder the terms: -150 + 150 + 10x2 + x4 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + 10x2 + x4 = 0 + 150 10x2 + x4 = 0 + 150 Combine like terms: 0 + 150 = 150 10x2 + x4 = 150 The x term is 10x2. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x2 + 25 + x4 = 150 + 25 Reorder the terms: 25 + 10x2 + x4 = 150 + 25 Combine like terms: 150 + 25 = 175 25 + 10x2 + x4 = 175 Factor a perfect square on the left side: (x2 + 5)(x2 + 5) = 175 Calculate the square root of the right side: 13.228756555 Break this problem into two subproblems by setting (x2 + 5) equal to 13.228756555 and -13.228756555.Subproblem 1
x2 + 5 = 13.228756555 Simplifying x2 + 5 = 13.228756555 Reorder the terms: 5 + x2 = 13.228756555 Solving 5 + x2 = 13.228756555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x2 = 13.228756555 + -5 Combine like terms: 5 + -5 = 0 0 + x2 = 13.228756555 + -5 x2 = 13.228756555 + -5 Combine like terms: 13.228756555 + -5 = 8.228756555 x2 = 8.228756555 Simplifying x2 = 8.228756555 Take the square root of each side: x = {-2.868580931, 2.868580931}Subproblem 2
x2 + 5 = -13.228756555 Simplifying x2 + 5 = -13.228756555 Reorder the terms: 5 + x2 = -13.228756555 Solving 5 + x2 = -13.228756555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x2 = -13.228756555 + -5 Combine like terms: 5 + -5 = 0 0 + x2 = -13.228756555 + -5 x2 = -13.228756555 + -5 Combine like terms: -13.228756555 + -5 = -18.228756555 x2 = -18.228756555 Simplifying x2 = -18.228756555 Reorder the terms: 18.228756555 + x2 = -18.228756555 + 18.228756555 Combine like terms: -18.228756555 + 18.228756555 = 0.000000000 18.228756555 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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