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: Identify quadratic coefficients

$a=2, b=3, c=-8$

Step3: Apply quadratic formula

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

Step4: Calculate discriminant

$\sqrt{3^2 - 4(2)(-8)} = \sqrt{9 + 64} = \sqrt{73} \approx 8.544$

Step5: Compute two solutions

$x = \frac{-3 + 8.544}{4} \approx 1.39$, $x = \frac{-3 - 8.544}{4} \approx -2.89$

Answer:

$x \approx 1.39, x \approx -2.89$