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Simplifying 0 = x4 + 26x2 + 165 Reorder the terms: 0 = 165 + 26x2 + x4 Solving 0 = 165 + 26x2 + x4 Solving for variable 'x'. Combine like terms: 0 + -165 = -165 -165 + -26x2 + -1x4 = 165 + 26x2 + x4 + -165 + -26x2 + -1x4 Reorder the terms: -165 + -26x2 + -1x4 = 165 + -165 + 26x2 + -26x2 + x4 + -1x4 Combine like terms: 165 + -165 = 0 -165 + -26x2 + -1x4 = 0 + 26x2 + -26x2 + x4 + -1x4 -165 + -26x2 + -1x4 = 26x2 + -26x2 + x4 + -1x4 Combine like terms: 26x2 + -26x2 = 0 -165 + -26x2 + -1x4 = 0 + x4 + -1x4 -165 + -26x2 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 -165 + -26x2 + -1x4 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(165 + 26x2 + x4) = 0 Factor a trinomial. -1((15 + x2)(11 + x2)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(15 + x2)' equal to zero and attempt to solve: Simplifying 15 + x2 = 0 Solving 15 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + x2 = 0 + -15 x2 = 0 + -15 Combine like terms: 0 + -15 = -15 x2 = -15 Simplifying x2 = -15 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 '(11 + x2)' equal to zero and attempt to solve: Simplifying 11 + x2 = 0 Solving 11 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + x2 = 0 + -11 x2 = 0 + -11 Combine like terms: 0 + -11 = -11 x2 = -11 Simplifying x2 = -11 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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