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Simplifying x4 + 15x2 + -49 = 0 Reorder the terms: -49 + 15x2 + x4 = 0 Solving -49 + 15x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 15x2 + 49 + x4 = 0 + 49 Reorder the terms: -49 + 49 + 15x2 + x4 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 15x2 + x4 = 0 + 49 15x2 + x4 = 0 + 49 Combine like terms: 0 + 49 = 49 15x2 + x4 = 49 The x term is 15x2. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x2 + 56.25 + x4 = 49 + 56.25 Reorder the terms: 56.25 + 15x2 + x4 = 49 + 56.25 Combine like terms: 49 + 56.25 = 105.25 56.25 + 15x2 + x4 = 105.25 Factor a perfect square on the left side: (x2 + 7.5)(x2 + 7.5) = 105.25 Calculate the square root of the right side: 10.259142264 Break this problem into two subproblems by setting (x2 + 7.5) equal to 10.259142264 and -10.259142264.Subproblem 1
x2 + 7.5 = 10.259142264 Simplifying x2 + 7.5 = 10.259142264 Reorder the terms: 7.5 + x2 = 10.259142264 Solving 7.5 + x2 = 10.259142264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x2 = 10.259142264 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x2 = 10.259142264 + -7.5 x2 = 10.259142264 + -7.5 Combine like terms: 10.259142264 + -7.5 = 2.759142264 x2 = 2.759142264 Simplifying x2 = 2.759142264 Take the square root of each side: x = {-1.661066604, 1.661066604}Subproblem 2
x2 + 7.5 = -10.259142264 Simplifying x2 + 7.5 = -10.259142264 Reorder the terms: 7.5 + x2 = -10.259142264 Solving 7.5 + x2 = -10.259142264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x2 = -10.259142264 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x2 = -10.259142264 + -7.5 x2 = -10.259142264 + -7.5 Combine like terms: -10.259142264 + -7.5 = -17.759142264 x2 = -17.759142264 Simplifying x2 = -17.759142264 Reorder the terms: 17.759142264 + x2 = -17.759142264 + 17.759142264 Combine like terms: -17.759142264 + 17.759142264 = 0.000000000 17.759142264 + 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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