Question

Find the solutions to the equation below
Check all that apply.
2x2 +9x + 4 = 0

Answer 1

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

Answer 2

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