Find the solutions to the equation below

Check all that apply.

2x2 + 9x + 4 = 0

in this case

a=2 b=9 c4

for this equation we have the formula

x1/2 = (-b + - (root of) b2 - 4ac) / 2a

x1/2 = (-9 + - (root of) 81 - 4*2*4) / 2*2

x1/2 = (-9 + - (root of) 81-32) / 4

x1/2 = (-9 + - (root of) 49/4

x1/2 = (-9 + - 7) / 4

x1 = - 9+7/4

x1=-2/4

x1=-1/2

x2 = - 9-7/4

x2 = - 16/4

x2 = - 4

Step-by-step explanation:

Use quadratic formula:

x = ((-b+-sqrt (b^2-4ac)) / 2a

x = ((-9+-sqrt (9^2-4 (2) (4)) / 2 (2)

x = ((-9+-sqrt (81-32)) / 4

x = ((-9+-sqrt (49)) / 4

x = (-9+-7) / 4

Solution 1:

x=-2/4

x=-1/2

Solution 2:

x=-16/4

x=-4

Now we check:

2 (-1/2) ^2+9 (-1/2) + 4=2/4+-9/2+4=1/2+-9/2+4=-8/2+4=-4+4=0 (x=-1/2 works)

2 (-4) ^2+9 (-4) + 4=2 (16) + (-36) + 4=32-36+4=-4+4=0 (x=-4 works)

So the solutions of the equation are x=-1/2 and x=-4