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Simplifying 21x4 + -53x3 + 26x2 = 0 Reorder the terms: 26x2 + -53x3 + 21x4 = 0 Solving 26x2 + -53x3 + 21x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(26 + -53x + 21x2) = 0 Factor a trinomial. x2((2 + -3x)(13 + -7x)) = 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 '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Subproblem 3
Set the factor '(13 + -7x)' equal to zero and attempt to solve: Simplifying 13 + -7x = 0 Solving 13 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -7x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -7x = 0 + -13 -7x = 0 + -13 Combine like terms: 0 + -13 = -13 -7x = -13 Divide each side by '-7'. x = 1.857142857 Simplifying x = 1.857142857Solution
x = {0, 0.6666666667, 1.857142857}
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