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Simplifying 7a2 + 32 = 7 + -40a Reorder the terms: 32 + 7a2 = 7 + -40a Solving 32 + 7a2 = 7 + -40a Solving for variable 'a'. Reorder the terms: 32 + -7 + 40a + 7a2 = 7 + -40a + -7 + 40a Combine like terms: 32 + -7 = 25 25 + 40a + 7a2 = 7 + -40a + -7 + 40a Reorder the terms: 25 + 40a + 7a2 = 7 + -7 + -40a + 40a Combine like terms: 7 + -7 = 0 25 + 40a + 7a2 = 0 + -40a + 40a 25 + 40a + 7a2 = -40a + 40a Combine like terms: -40a + 40a = 0 25 + 40a + 7a2 = 0 Factor a trinomial. (5 + a)(5 + 7a) = 0Subproblem 1
Set the factor '(5 + a)' equal to zero and attempt to solve: Simplifying 5 + a = 0 Solving 5 + a = 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 + a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + a = 0 + -5 a = 0 + -5 Combine like terms: 0 + -5 = -5 a = -5 Simplifying a = -5Subproblem 2
Set the factor '(5 + 7a)' equal to zero and attempt to solve: Simplifying 5 + 7a = 0 Solving 5 + 7a = 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 + 7a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 7a = 0 + -5 7a = 0 + -5 Combine like terms: 0 + -5 = -5 7a = -5 Divide each side by '7'. a = -0.7142857143 Simplifying a = -0.7142857143Solution
a = {-5, -0.7142857143}
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