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Simplifying 2c4 + -46c2 + -100 = 0 Reorder the terms: -100 + -46c2 + 2c4 = 0 Solving -100 + -46c2 + 2c4 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '2'. 2(-50 + -23c2 + c4) = 0 Factor a trinomial. 2((-2 + -1c2)(25 + -1c2)) = 0 Factor a difference between two squares. 2((-2 + -1c2)((5 + c)(5 + -1c))) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -1c2)' equal to zero and attempt to solve: Simplifying -2 + -1c2 = 0 Solving -2 + -1c2 = 0 Move all terms containing c to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1c2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1c2 = 0 + 2 -1c2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1c2 = 2 Divide each side by '-1'. c2 = -2 Simplifying c2 = -2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(5 + c)' equal to zero and attempt to solve: Simplifying 5 + c = 0 Solving 5 + c = 0 Move all terms containing c to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + c = 0 + -5 Combine like terms: 5 + -5 = 0 0 + c = 0 + -5 c = 0 + -5 Combine like terms: 0 + -5 = -5 c = -5 Simplifying c = -5Subproblem 3
Set the factor '(5 + -1c)' equal to zero and attempt to solve: Simplifying 5 + -1c = 0 Solving 5 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1c = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1c = 0 + -5 -1c = 0 + -5 Combine like terms: 0 + -5 = -5 -1c = -5 Divide each side by '-1'. c = 5 Simplifying c = 5Solution
c = {-5, 5}
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