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Simplifying 1 + -3a(7a + 1) = -28 + 5a Reorder the terms: 1 + -3a(1 + 7a) = -28 + 5a 1 + (1 * -3a + 7a * -3a) = -28 + 5a 1 + (-3a + -21a2) = -28 + 5a Solving 1 + -3a + -21a2 = -28 + 5a Solving for variable 'a'. Reorder the terms: 1 + 28 + -3a + -5a + -21a2 = -28 + 5a + 28 + -5a Combine like terms: 1 + 28 = 29 29 + -3a + -5a + -21a2 = -28 + 5a + 28 + -5a Combine like terms: -3a + -5a = -8a 29 + -8a + -21a2 = -28 + 5a + 28 + -5a Reorder the terms: 29 + -8a + -21a2 = -28 + 28 + 5a + -5a Combine like terms: -28 + 28 = 0 29 + -8a + -21a2 = 0 + 5a + -5a 29 + -8a + -21a2 = 5a + -5a Combine like terms: 5a + -5a = 0 29 + -8a + -21a2 = 0 Factor a trinomial. (1 + -1a)(29 + 21a) = 0Subproblem 1
Set the factor '(1 + -1a)' equal to zero and attempt to solve: Simplifying 1 + -1a = 0 Solving 1 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1a = 0 + -1 -1a = 0 + -1 Combine like terms: 0 + -1 = -1 -1a = -1 Divide each side by '-1'. a = 1 Simplifying a = 1Subproblem 2
Set the factor '(29 + 21a)' equal to zero and attempt to solve: Simplifying 29 + 21a = 0 Solving 29 + 21a = 0 Move all terms containing a to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + 21a = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 21a = 0 + -29 21a = 0 + -29 Combine like terms: 0 + -29 = -29 21a = -29 Divide each side by '21'. a = -1.380952381 Simplifying a = -1.380952381Solution
a = {1, -1.380952381}
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