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