ANSWER
1.39
EXPLANATION
The given quadratic equation is
[tex]0 = 2 {x}^{2} + 3x - 8[/tex]
This is the same as,
[tex]2 {x}^{2} + 3x - 8 = 0[/tex]
Comparing to
[tex]a {x}^{2} + bx + c = 0[/tex]
We have
a=2, b=3,c=-8
Using the quadratic formula, the solution is given by:
[tex]x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
We substitute the values to get,
[tex]x = \frac{ - 3\pm \: \sqrt{ {3}^{2} - 4(2)( - 8)} }{2(2)} [/tex]
[tex]x = \frac{ - 3\pm \: \sqrt{ 73} }{4} [/tex]
The positive root is
[tex]x = \frac{ - 3 + \: \sqrt{ 73} }{4} = 1.39[/tex]
to the nearest hundredth.
