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Simplifying L(L + -5) = 176 Reorder the terms: L(-5 + L) = 176 (-5 * L + L * L) = 176 (-5L + L2) = 176 Solving -5L + L2 = 176 Solving for variable 'L'. Reorder the terms: -176 + -5L + L2 = 176 + -176 Combine like terms: 176 + -176 = 0 -176 + -5L + L2 = 0 Factor a trinomial. (-11 + -1L)(16 + -1L) = 0Subproblem 1
Set the factor '(-11 + -1L)' equal to zero and attempt to solve: Simplifying -11 + -1L = 0 Solving -11 + -1L = 0 Move all terms containing L to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -1L = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1L = 0 + 11 -1L = 0 + 11 Combine like terms: 0 + 11 = 11 -1L = 11 Divide each side by '-1'. L = -11 Simplifying L = -11Subproblem 2
Set the factor '(16 + -1L)' equal to zero and attempt to solve: Simplifying 16 + -1L = 0 Solving 16 + -1L = 0 Move all terms containing L to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + -1L = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -1L = 0 + -16 -1L = 0 + -16 Combine like terms: 0 + -16 = -16 -1L = -16 Divide each side by '-1'. L = 16 Simplifying L = 16Solution
L = {-11, 16}
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