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Simplifying (a + -2)(a + 7) + -70 = 0 Reorder the terms: (-2 + a)(a + 7) + -70 = 0 Reorder the terms: (-2 + a)(7 + a) + -70 = 0 Multiply (-2 + a) * (7 + a) (-2(7 + a) + a(7 + a)) + -70 = 0 ((7 * -2 + a * -2) + a(7 + a)) + -70 = 0 ((-14 + -2a) + a(7 + a)) + -70 = 0 (-14 + -2a + (7 * a + a * a)) + -70 = 0 (-14 + -2a + (7a + a2)) + -70 = 0 Combine like terms: -2a + 7a = 5a (-14 + 5a + a2) + -70 = 0 Reorder the terms: -14 + -70 + 5a + a2 = 0 Combine like terms: -14 + -70 = -84 -84 + 5a + a2 = 0 Solving -84 + 5a + a2 = 0 Solving for variable 'a'. Factor a trinomial. (-12 + -1a)(7 + -1a) = 0Subproblem 1
Set the factor '(-12 + -1a)' equal to zero and attempt to solve: Simplifying -12 + -1a = 0 Solving -12 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1a = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1a = 0 + 12 -1a = 0 + 12 Combine like terms: 0 + 12 = 12 -1a = 12 Divide each side by '-1'. a = -12 Simplifying a = -12Subproblem 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 = {-12, 7}
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