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Simplifying x4 + 13x3 = -36x2 Reorder the terms: 13x3 + x4 = -36x2 Solving 13x3 + x4 = -36x2 Solving for variable 'x'. Reorder the terms: 36x2 + 13x3 + x4 = -36x2 + 36x2 Combine like terms: -36x2 + 36x2 = 0 36x2 + 13x3 + x4 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(36 + 13x + x2) = 0 Factor a trinomial. x2((9 + x)(4 + x)) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Simplifying x = -9Subproblem 3
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {0, -9, -4}
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