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Simplifying X4 + -10X2 + -25 = 0 Reorder the terms: -25 + -10X2 + X4 = 0 Solving -25 + -10X2 + X4 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -10X2 + 25 + X4 = 0 + 25 Reorder the terms: -25 + 25 + -10X2 + X4 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -10X2 + X4 = 0 + 25 -10X2 + X4 = 0 + 25 Combine like terms: 0 + 25 = 25 -10X2 + X4 = 25 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 = 25 + 25 Reorder the terms: 25 + -10X2 + X4 = 25 + 25 Combine like terms: 25 + 25 = 50 25 + -10X2 + X4 = 50 Factor a perfect square on the left side: (X2 + -5)(X2 + -5) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (X2 + -5) equal to 7.071067812 and -7.071067812.Subproblem 1
X2 + -5 = 7.071067812 Simplifying X2 + -5 = 7.071067812 Reorder the terms: -5 + X2 = 7.071067812 Solving -5 + X2 = 7.071067812 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 = 7.071067812 + 5 Combine like terms: -5 + 5 = 0 0 + X2 = 7.071067812 + 5 X2 = 7.071067812 + 5 Combine like terms: 7.071067812 + 5 = 12.071067812 X2 = 12.071067812 Simplifying X2 = 12.071067812 Take the square root of each side: X = {-3.474344228, 3.474344228}Subproblem 2
X2 + -5 = -7.071067812 Simplifying X2 + -5 = -7.071067812 Reorder the terms: -5 + X2 = -7.071067812 Solving -5 + X2 = -7.071067812 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 = -7.071067812 + 5 Combine like terms: -5 + 5 = 0 0 + X2 = -7.071067812 + 5 X2 = -7.071067812 + 5 Combine like terms: -7.071067812 + 5 = -2.071067812 X2 = -2.071067812 Simplifying X2 = -2.071067812 Reorder the terms: 2.071067812 + X2 = -2.071067812 + 2.071067812 Combine like terms: -2.071067812 + 2.071067812 = 0.000000000 2.071067812 + 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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