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Simplifying x4 + 20x2 + -15 = 0 Reorder the terms: -15 + 20x2 + x4 = 0 Solving -15 + 20x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 20x2 + 15 + x4 = 0 + 15 Reorder the terms: -15 + 15 + 20x2 + x4 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 20x2 + x4 = 0 + 15 20x2 + x4 = 0 + 15 Combine like terms: 0 + 15 = 15 20x2 + x4 = 15 The x term is 20x2. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x2 + 100 + x4 = 15 + 100 Reorder the terms: 100 + 20x2 + x4 = 15 + 100 Combine like terms: 15 + 100 = 115 100 + 20x2 + x4 = 115 Factor a perfect square on the left side: (x2 + 10)(x2 + 10) = 115 Calculate the square root of the right side: 10.723805295 Break this problem into two subproblems by setting (x2 + 10) equal to 10.723805295 and -10.723805295.Subproblem 1
x2 + 10 = 10.723805295 Simplifying x2 + 10 = 10.723805295 Reorder the terms: 10 + x2 = 10.723805295 Solving 10 + x2 = 10.723805295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x2 = 10.723805295 + -10 Combine like terms: 10 + -10 = 0 0 + x2 = 10.723805295 + -10 x2 = 10.723805295 + -10 Combine like terms: 10.723805295 + -10 = 0.723805295 x2 = 0.723805295 Simplifying x2 = 0.723805295 Take the square root of each side: x = {-0.850767474, 0.850767474}Subproblem 2
x2 + 10 = -10.723805295 Simplifying x2 + 10 = -10.723805295 Reorder the terms: 10 + x2 = -10.723805295 Solving 10 + x2 = -10.723805295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x2 = -10.723805295 + -10 Combine like terms: 10 + -10 = 0 0 + x2 = -10.723805295 + -10 x2 = -10.723805295 + -10 Combine like terms: -10.723805295 + -10 = -20.723805295 x2 = -20.723805295 Simplifying x2 = -20.723805295 Reorder the terms: 20.723805295 + x2 = -20.723805295 + 20.723805295 Combine like terms: -20.723805295 + 20.723805295 = 0.000000000 20.723805295 + 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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