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Simplifying 5x5 + 2x3 = 7x Reorder the terms: 2x3 + 5x5 = 7x Solving 2x3 + 5x5 = 7x Solving for variable 'x'. Reorder the terms: -7x + 2x3 + 5x5 = 7x + -7x Combine like terms: 7x + -7x = 0 -7x + 2x3 + 5x5 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-7 + 2x2 + 5x4) = 0 Factor a trinomial. x((-7 + -5x2)(1 + -1x2)) = 0 Factor a difference between two squares. x((-7 + -5x2)((1 + x)(1 + -1x))) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-7 + -5x2)' equal to zero and attempt to solve: Simplifying -7 + -5x2 = 0 Solving -7 + -5x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -5x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -5x2 = 0 + 7 -5x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -5x2 = 7 Divide each side by '-5'. x2 = -1.4 Simplifying x2 = -1.4 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Subproblem 4
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {0, -1, 1}
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