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Simplifying 4a2 = 7a + 30 Reorder the terms: 4a2 = 30 + 7a Solving 4a2 = 30 + 7a Solving for variable 'a'. Reorder the terms: -30 + -7a + 4a2 = 30 + 7a + -30 + -7a Reorder the terms: -30 + -7a + 4a2 = 30 + -30 + 7a + -7a Combine like terms: 30 + -30 = 0 -30 + -7a + 4a2 = 0 + 7a + -7a -30 + -7a + 4a2 = 7a + -7a Combine like terms: 7a + -7a = 0 -30 + -7a + 4a2 = 0 Factor a trinomial. (-2 + -1a)(15 + -4a) = 0Subproblem 1
Set the factor '(-2 + -1a)' equal to zero and attempt to solve: Simplifying -2 + -1a = 0 Solving -2 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1a = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1a = 0 + 2 -1a = 0 + 2 Combine like terms: 0 + 2 = 2 -1a = 2 Divide each side by '-1'. a = -2 Simplifying a = -2Subproblem 2
Set the factor '(15 + -4a)' equal to zero and attempt to solve: Simplifying 15 + -4a = 0 Solving 15 + -4a = 0 Move all terms containing a to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -4a = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -4a = 0 + -15 -4a = 0 + -15 Combine like terms: 0 + -15 = -15 -4a = -15 Divide each side by '-4'. a = 3.75 Simplifying a = 3.75Solution
a = {-2, 3.75}
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