Answer:
There are two solutions.
[tex]x_1 = -0.5\\x_2 = -2[/tex]
Step-by-step explanation:
Step 1
Use the formula of ax^2 + bx + c = 0 to find the coefficients.
[tex]a = 2\\b = 5\\c = 2[/tex]
Step 2
[tex]x=\frac{ (-b+/-sqrt(b^2-4ac))}{(2a)}\\x=\frac{ (-5 +/- sqrt(5^2-4*2*2))}{(2*2)}\\x=\frac{(-5 +/- sqrt(25-4*2*2))}{(2*2)}\\x=\frac{(-5 +/- sqrt(25-8*2))}{(2*2)}\\x=\frac{(-5 +/- sqrt(9))}{(2*2)}[/tex]
[tex]x = \frac{-5 +/- \sqrt{9} }{4}[/tex]
Step 3
[tex]9 = 3^2\\\sqrt{9} = \sqrt{3*3}\\\sqrt{3*3} = \sqrt{3^2}\\\sqrt{3^2} = 3[/tex]
Step 4
[tex]x_1=\frac{(-5+3)}{4} -- > x_2=\frac{(-5-3)}{4}\\x_1=\frac{(-5+3)}{4}\\x_1=\frac{-2}{4}\\x_1=-0,5[/tex]
[tex]x_2=\frac{(-5-3)}{4}\\x_2=\frac{(-8)}{4}[/tex]
[tex]x_2=-2[/tex]
Hope this helps.
