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Simplifying x4 + 2x2 + -7.5 = 0 Reorder the terms: -7.5 + 2x2 + x4 = 0 Solving -7.5 + 2x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 2x2 + 7.5 + x4 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 2x2 + x4 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 2x2 + x4 = 0 + 7.5 2x2 + x4 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 2x2 + x4 = 7.5 The x term is 2x2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x2 + 1 + x4 = 7.5 + 1 Reorder the terms: 1 + 2x2 + x4 = 7.5 + 1 Combine like terms: 7.5 + 1 = 8.5 1 + 2x2 + x4 = 8.5 Factor a perfect square on the left side: (x2 + 1)(x2 + 1) = 8.5 Calculate the square root of the right side: 2.915475947 Break this problem into two subproblems by setting (x2 + 1) equal to 2.915475947 and -2.915475947.Subproblem 1
x2 + 1 = 2.915475947 Simplifying x2 + 1 = 2.915475947 Reorder the terms: 1 + x2 = 2.915475947 Solving 1 + x2 = 2.915475947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = 2.915475947 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 2.915475947 + -1 x2 = 2.915475947 + -1 Combine like terms: 2.915475947 + -1 = 1.915475947 x2 = 1.915475947 Simplifying x2 = 1.915475947 Take the square root of each side: x = {-1.384007206, 1.384007206}Subproblem 2
x2 + 1 = -2.915475947 Simplifying x2 + 1 = -2.915475947 Reorder the terms: 1 + x2 = -2.915475947 Solving 1 + x2 = -2.915475947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = -2.915475947 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = -2.915475947 + -1 x2 = -2.915475947 + -1 Combine like terms: -2.915475947 + -1 = -3.915475947 x2 = -3.915475947 Simplifying x2 = -3.915475947 Reorder the terms: 3.915475947 + x2 = -3.915475947 + 3.915475947 Combine like terms: -3.915475947 + 3.915475947 = 0.000000000 3.915475947 + 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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