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}
