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Simplifying 5x4 + -152x3 + 1083x2 = 0 Reorder the terms: 1083x2 + -152x3 + 5x4 = 0 Solving 1083x2 + -152x3 + 5x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(1083 + -152x + 5x2) = 0 Factor a trinomial. x2((57 + -5x)(19 + -1x)) = 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 '(57 + -5x)' equal to zero and attempt to solve: Simplifying 57 + -5x = 0 Solving 57 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-57' to each side of the equation. 57 + -57 + -5x = 0 + -57 Combine like terms: 57 + -57 = 0 0 + -5x = 0 + -57 -5x = 0 + -57 Combine like terms: 0 + -57 = -57 -5x = -57 Divide each side by '-5'. x = 11.4 Simplifying x = 11.4Subproblem 3
Set the factor '(19 + -1x)' equal to zero and attempt to solve: Simplifying 19 + -1x = 0 Solving 19 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + -1x = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -1x = 0 + -19 -1x = 0 + -19 Combine like terms: 0 + -19 = -19 -1x = -19 Divide each side by '-1'. x = 19 Simplifying x = 19Solution
x = {0, 11.4, 19}
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