Answer :
[tex]2x^2-3x-2=0 \\
2x^2-4x+x-2=0 \\
2x(x-2)+1(x-2)=0 \\
(2x+1)(x-2)=0 \\
2x+1=0 \ \lor \ x-2=0 \\
2x=-1 \ \lor \ x=2 \\
x=-\frac{1}{2} \ \lor \ x=2 \\
\boxed{x=-\frac{1}{2} \hbox{ or } x=2}[/tex]
2x² - 3x - 2 = 0
x = -(-3) +/- √((-3)² - 4(2)(-2))
2(2)
x = 3 +/- √(9 + 16)
4
x = 3 +/- √(25)
4
x = 3 +/- 5
4
x = 3 + 5 or x = 3 - 5
4 4
x = 8 x = -2
4 4
x = 2 x = ⁻¹/₂
x = -(-3) +/- √((-3)² - 4(2)(-2))
2(2)
x = 3 +/- √(9 + 16)
4
x = 3 +/- √(25)
4
x = 3 +/- 5
4
x = 3 + 5 or x = 3 - 5
4 4
x = 8 x = -2
4 4
x = 2 x = ⁻¹/₂
