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Simplifying 10x6 + -53x4 + 36x2 = 0 Reorder the terms: 36x2 + -53x4 + 10x6 = 0 Solving 36x2 + -53x4 + 10x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(36 + -53x2 + 10x4) = 0 Factor a trinomial. x2((4 + -5x2)(9 + -2x2)) = 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 '(4 + -5x2)' equal to zero and attempt to solve: Simplifying 4 + -5x2 = 0 Solving 4 + -5x2 = 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 + -5x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5x2 = 0 + -4 -5x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -5x2 = -4 Divide each side by '-5'. x2 = 0.8 Simplifying x2 = 0.8 Take the square root of each side: x = {-0.894427191, 0.894427191}Subproblem 3
Set the factor '(9 + -2x2)' equal to zero and attempt to solve: Simplifying 9 + -2x2 = 0 Solving 9 + -2x2 = 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 + -2x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2x2 = 0 + -9 -2x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -2x2 = -9 Divide each side by '-2'. x2 = 4.5 Simplifying x2 = 4.5 Take the square root of each side: x = {-2.121320344, 2.121320344}Solution
x = {0, -0.894427191, 0.894427191, -2.121320344, 2.121320344}
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