Question

solve the equation by factoring, using tables, or by graphing.
$2x^2 + 5x = 9$
$x = \square$
(simplify your answer. type an integer or a decimal rounded to the nearest hundredth as needed. use a comma to

Explanation:

Step1: Rearrange to standard quadratic form

$2x^2 + 5x - 9 = 0$

Step2: Apply quadratic formula

For $ax^2+bx+c=0$, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$. Here $a=2$, $b=5$, $c=-9$.
$$x=\frac{-5\pm\sqrt{5^2-4(2)(-9)}}{2(2)}$$

Step3: Calculate discriminant

$\sqrt{25 + 72}=\sqrt{97}\approx9.849$

Step4: Compute two solutions

$x_1=\frac{-5 + 9.849}{4}\approx\frac{4.849}{4}\approx1.21$
$x_2=\frac{-5 - 9.849}{4}\approx\frac{-14.849}{4}\approx-3.71$

Answer:

$1.21, -3.71$