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Simplifying (L + 10) * L = 1064 Reorder the terms: (10 + L) * L = 1064 Reorder the terms for easier multiplication: L(10 + L) = 1064 (10 * L + L * L) = 1064 (10L + L2) = 1064 Solving 10L + L2 = 1064 Solving for variable 'L'. Reorder the terms: -1064 + 10L + L2 = 1064 + -1064 Combine like terms: 1064 + -1064 = 0 -1064 + 10L + L2 = 0 Factor a trinomial. (-38 + -1L)(28 + -1L) = 0Subproblem 1
Set the factor '(-38 + -1L)' equal to zero and attempt to solve: Simplifying -38 + -1L = 0 Solving -38 + -1L = 0 Move all terms containing L to the left, all other terms to the right. Add '38' to each side of the equation. -38 + 38 + -1L = 0 + 38 Combine like terms: -38 + 38 = 0 0 + -1L = 0 + 38 -1L = 0 + 38 Combine like terms: 0 + 38 = 38 -1L = 38 Divide each side by '-1'. L = -38 Simplifying L = -38Subproblem 2
Set the factor '(28 + -1L)' equal to zero and attempt to solve: Simplifying 28 + -1L = 0 Solving 28 + -1L = 0 Move all terms containing L to the left, all other terms to the right. Add '-28' to each side of the equation. 28 + -28 + -1L = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -1L = 0 + -28 -1L = 0 + -28 Combine like terms: 0 + -28 = -28 -1L = -28 Divide each side by '-1'. L = 28 Simplifying L = 28Solution
L = {-38, 28}
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