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Simplifying 4a(a + 1) = 35 Reorder the terms: 4a(1 + a) = 35 (1 * 4a + a * 4a) = 35 (4a + 4a2) = 35 Solving 4a + 4a2 = 35 Solving for variable 'a'. Reorder the terms: -35 + 4a + 4a2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + 4a + 4a2 = 0 Factor a trinomial. (-7 + -2a)(5 + -2a) = 0Subproblem 1
Set the factor '(-7 + -2a)' equal to zero and attempt to solve: Simplifying -7 + -2a = 0 Solving -7 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -2a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2a = 0 + 7 -2a = 0 + 7 Combine like terms: 0 + 7 = 7 -2a = 7 Divide each side by '-2'. a = -3.5 Simplifying a = -3.5Subproblem 2
Set the factor '(5 + -2a)' equal to zero and attempt to solve: Simplifying 5 + -2a = 0 Solving 5 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2a = 0 + -5 -2a = 0 + -5 Combine like terms: 0 + -5 = -5 -2a = -5 Divide each side by '-2'. a = 2.5 Simplifying a = 2.5Solution
a = {-3.5, 2.5}
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