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Simplifying 35 = c(c + -2) Reorder the terms: 35 = c(-2 + c) 35 = (-2 * c + c * c) 35 = (-2c + c2) Solving 35 = -2c + c2 Solving for variable 'c'. Reorder the terms: 35 + 2c + -1c2 = -2c + 2c + c2 + -1c2 Combine like terms: -2c + 2c = 0 35 + 2c + -1c2 = 0 + c2 + -1c2 35 + 2c + -1c2 = c2 + -1c2 Combine like terms: c2 + -1c2 = 0 35 + 2c + -1c2 = 0 Factor a trinomial. (7 + -1c)(5 + c) = 0Subproblem 1
Set the factor '(7 + -1c)' equal to zero and attempt to solve: Simplifying 7 + -1c = 0 Solving 7 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1c = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1c = 0 + -7 -1c = 0 + -7 Combine like terms: 0 + -7 = -7 -1c = -7 Divide each side by '-1'. c = 7 Simplifying c = 7Subproblem 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 = -5Solution
c = {7, -5}
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