Question

Earn Some MAD Points~!

Answer 1

Simplifying (3a2 + -2a + 4) + -1(a2 + -3a + 7) = 0 Reorder the terms: (4 + -2a + 3a2) + -1(a2 + -3a + 7) = 0 Remove parenthesis around (4 + -2a + 3a2) 4 + -2a + 3a2 + -1(a2 + -3a + 7) = 0 Reorder the terms: 4 + -2a + 3a2 + -1(7 + -3a + a2) = 0 4 + -2a + 3a2 + (7 * -1 + -3a * -1 + a2 * -1) = 0 4 + -2a + 3a2 + (-7 + 3a + -1a2) = 0 Reorder the terms: 4 + -7 + -2a + 3a + 3a2 + -1a2 = 0 Combine like terms: 4 + -7 = -3 -3 + -2a + 3a + 3a2 + -1a2 = 0 Combine like terms: -2a + 3a = 1a -3 + 1a + 3a2 + -1a2 = 0 Combine like terms: 3a2 + -1a2 = 2a2 -3 + 1a + 2a2 = 0 Solving -3 + 1a + 2a2 = 0 Solving for variable 'a'. Factor a trinomial. (-3 + -2a)(1 + -1a) = 0 Subproblem 1Set the factor '(-3 + -2a)' equal to zero and attempt to solve: Simplifying -3 + -2a = 0 Solving -3 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -2a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2a = 0 + 3 -2a = 0 + 3 Combine like terms: 0 + 3 = 3 -2a = 3 Divide each side by '-2'. a = -1.5 Simplifying a = -1.5 Subproblem 2Set 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 = 1Solutiona = {-1.5, 1}