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Simplifying 7a2 = 49 + 42a Solving 7a2 = 49 + 42a Solving for variable 'a'. Reorder the terms: -49 + -42a + 7a2 = 49 + 42a + -49 + -42a Reorder the terms: -49 + -42a + 7a2 = 49 + -49 + 42a + -42a Combine like terms: 49 + -49 = 0 -49 + -42a + 7a2 = 0 + 42a + -42a -49 + -42a + 7a2 = 42a + -42a Combine like terms: 42a + -42a = 0 -49 + -42a + 7a2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-7 + -6a + a2) = 0 Factor a trinomial. 7((-1 + -1a)(7 + -1a)) = 0 Ignore the factor 7.Subproblem 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 '(7 + -1a)' equal to zero and attempt to solve: Simplifying 7 + -1a = 0 Solving 7 + -1a = 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 + -1a = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1a = 0 + -7 -1a = 0 + -7 Combine like terms: 0 + -7 = -7 -1a = -7 Divide each side by '-1'. a = 7 Simplifying a = 7Solution
a = {-1, 7}
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