Question

solve the equation by factoring, using tables, or by graphing
$2x^2 + 3x - 8$
$x = \square$
(simplify your answer. type an integer or a decimal rounded to the nearest hundredth as needed. use a comma to separate answers as needed.)

Explanation:

Step1: Set equation to zero

$2x^2 + 3x - 8 = 0$

Step2: Apply quadratic formula

For $ax^2+bx+c=0$, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Here $a=2, b=3, c=-8$, so:
$$x=\frac{-3\pm\sqrt{3^2-4(2)(-8)}}{2(2)}$$

Step3: Calculate discriminant

$\sqrt{9 + 64} = \sqrt{73} \approx 8.544$

Step4: Compute two solutions

$x_1=\frac{-3 + 8.544}{4}\approx\frac{5.544}{4}\approx1.39$
$x_2=\frac{-3 - 8.544}{4}\approx\frac{-11.544}{4}\approx-2.89$

Answer:

$x = 1.39, x = -2.89$