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Simplifying (1 + 4c)(1 + 4c) = 0 Multiply (1 + 4c) * (1 + 4c) (1(1 + 4c) + 4c * (1 + 4c)) = 0 ((1 * 1 + 4c * 1) + 4c * (1 + 4c)) = 0 ((1 + 4c) + 4c * (1 + 4c)) = 0 (1 + 4c + (1 * 4c + 4c * 4c)) = 0 (1 + 4c + (4c + 16c2)) = 0 Combine like terms: 4c + 4c = 8c (1 + 8c + 16c2) = 0 Solving 1 + 8c + 16c2 = 0 Solving for variable 'c'. Factor a trinomial. (1 + 4c)(1 + 4c) = 0Subproblem 1
Set the factor '(1 + 4c)' equal to zero and attempt to solve: Simplifying 1 + 4c = 0 Solving 1 + 4c = 0 Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 4c = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4c = 0 + -1 4c = 0 + -1 Combine like terms: 0 + -1 = -1 4c = -1 Divide each side by '4'. c = -0.25 Simplifying c = -0.25Subproblem 2
Set the factor '(1 + 4c)' equal to zero and attempt to solve: Simplifying 1 + 4c = 0 Solving 1 + 4c = 0 Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 4c = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4c = 0 + -1 4c = 0 + -1 Combine like terms: 0 + -1 = -1 4c = -1 Divide each side by '4'. c = -0.25 Simplifying c = -0.25Solution
c = {-0.25, -0.25}
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