Question

find the solution set.
2x² + 5x + 2 = 0
separate the two values with a comma.
enter the correct answer.

Explanation:

Step1: Identify quadratic formula

For $ax^2+bx+c=0$, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Step2: Assign a,b,c values

$a=2$, $b=5$, $c=2$

Step3: Calculate discriminant

$\Delta = 5^2-4(2)(2)=25-16=9$

Step4: Compute first root

$x_1=\frac{-5+\sqrt{9}}{2(2)}=\frac{-5+3}{4}=\frac{-2}{4}=-\frac{1}{2}$

Step5: Compute second root

$x_2=\frac{-5-\sqrt{9}}{2(2)}=\frac{-5-3}{4}=\frac{-8}{4}=-2$

Answer:

$-2, -\frac{1}{2}$