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Simplifying c2 + -2c = 40 + 4c Reorder the terms: -2c + c2 = 40 + 4c Solving -2c + c2 = 40 + 4c Solving for variable 'c'. Reorder the terms: -40 + -2c + -4c + c2 = 40 + 4c + -40 + -4c Combine like terms: -2c + -4c = -6c -40 + -6c + c2 = 40 + 4c + -40 + -4c Reorder the terms: -40 + -6c + c2 = 40 + -40 + 4c + -4c Combine like terms: 40 + -40 = 0 -40 + -6c + c2 = 0 + 4c + -4c -40 + -6c + c2 = 4c + -4c Combine like terms: 4c + -4c = 0 -40 + -6c + c2 = 0 Factor a trinomial. (-4 + -1c)(10 + -1c) = 0Subproblem 1
Set the factor '(-4 + -1c)' equal to zero and attempt to solve: Simplifying -4 + -1c = 0 Solving -4 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1c = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1c = 0 + 4 -1c = 0 + 4 Combine like terms: 0 + 4 = 4 -1c = 4 Divide each side by '-1'. c = -4 Simplifying c = -4Subproblem 2
Set the factor '(10 + -1c)' equal to zero and attempt to solve: Simplifying 10 + -1c = 0 Solving 10 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1c = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1c = 0 + -10 -1c = 0 + -10 Combine like terms: 0 + -10 = -10 -1c = -10 Divide each side by '-1'. c = 10 Simplifying c = 10Solution
c = {-4, 10}
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