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Simplifying 0 = x4 + 26x2 + 25 Reorder the terms: 0 = 25 + 26x2 + x4 Solving 0 = 25 + 26x2 + x4 Solving for variable 'x'. Combine like terms: 0 + -25 = -25 -25 + -26x2 + -1x4 = 25 + 26x2 + x4 + -25 + -26x2 + -1x4 Reorder the terms: -25 + -26x2 + -1x4 = 25 + -25 + 26x2 + -26x2 + x4 + -1x4 Combine like terms: 25 + -25 = 0 -25 + -26x2 + -1x4 = 0 + 26x2 + -26x2 + x4 + -1x4 -25 + -26x2 + -1x4 = 26x2 + -26x2 + x4 + -1x4 Combine like terms: 26x2 + -26x2 = 0 -25 + -26x2 + -1x4 = 0 + x4 + -1x4 -25 + -26x2 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 -25 + -26x2 + -1x4 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(25 + 26x2 + x4) = 0 Factor a trinomial. -1((25 + x2)(1 + x2)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(25 + x2)' equal to zero and attempt to solve: Simplifying 25 + x2 = 0 Solving 25 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + x2 = 0 + -25 x2 = 0 + -25 Combine like terms: 0 + -25 = -25 x2 = -25 Simplifying x2 = -25 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(1 + x2)' equal to zero and attempt to solve: Simplifying 1 + x2 = 0 Solving 1 + x2 = 0 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 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 0 + -1 x2 = 0 + -1 Combine like terms: 0 + -1 = -1 x2 = -1 Simplifying x2 = -1 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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