Question

Completing the square
v^2 + 4v - 22= 10

Answer 1

v² + 4v - 22 = 10
- 10 - 10
v² + 4v - 32 = 0
v = -4 +/- √(4² - 4(1)(-32))
2(1)
v = -4 +/- √(16 + 128)
2
v = -4 +/- √(144)
2
v = -4 +/- 12
2
v = -2 +/- 6
v = -2 + 6 ∨ v = -2 - 6
v = 4 ∨ v = -8

Answer 2

`v^2+4v-22=10 \\ v^2+4v+4-4-22=10 \\ (v+2)^2-26=10 \\ (v+2)^2=36 \\ √((v+2)^2)=√(36) \\ |v+2|=6 \\ v+2=6 \ \lor \ v+2=-6 \\ v=4 \ \lor \ v=-8 \\ \boxed{v=-8 \hbox{ or } v=4}`