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Simplifying x4 + -15x2 + -36 = 0 Reorder the terms: -36 + -15x2 + x4 = 0 Solving -36 + -15x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -15x2 + 36 + x4 = 0 + 36 Reorder the terms: -36 + 36 + -15x2 + x4 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -15x2 + x4 = 0 + 36 -15x2 + x4 = 0 + 36 Combine like terms: 0 + 36 = 36 -15x2 + x4 = 36 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 = 36 + 56.25 Reorder the terms: 56.25 + -15x2 + x4 = 36 + 56.25 Combine like terms: 36 + 56.25 = 92.25 56.25 + -15x2 + x4 = 92.25 Factor a perfect square on the left side: (x2 + -7.5)(x2 + -7.5) = 92.25 Calculate the square root of the right side: 9.604686356 Break this problem into two subproblems by setting (x2 + -7.5) equal to 9.604686356 and -9.604686356.Subproblem 1
x2 + -7.5 = 9.604686356 Simplifying x2 + -7.5 = 9.604686356 Reorder the terms: -7.5 + x2 = 9.604686356 Solving -7.5 + x2 = 9.604686356 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 = 9.604686356 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x2 = 9.604686356 + 7.5 x2 = 9.604686356 + 7.5 Combine like terms: 9.604686356 + 7.5 = 17.104686356 x2 = 17.104686356 Simplifying x2 = 17.104686356 Take the square root of each side: x = {-4.135781227, 4.135781227}Subproblem 2
x2 + -7.5 = -9.604686356 Simplifying x2 + -7.5 = -9.604686356 Reorder the terms: -7.5 + x2 = -9.604686356 Solving -7.5 + x2 = -9.604686356 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 = -9.604686356 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x2 = -9.604686356 + 7.5 x2 = -9.604686356 + 7.5 Combine like terms: -9.604686356 + 7.5 = -2.104686356 x2 = -2.104686356 Simplifying x2 = -2.104686356 Reorder the terms: 2.104686356 + x2 = -2.104686356 + 2.104686356 Combine like terms: -2.104686356 + 2.104686356 = 0.000000000 2.104686356 + 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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