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

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

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1