We will need to complete the square to solve this equation.
First move the constant to the other side of the equation by adding 22 to both sides.
8x^2+3x=28x2+3x=2
Factor out the coefficient, 88, from the x^2 term.
8(x^2+3/8x)=28(x2+38x)=2
Take the coefficient of the xx term and divide it by 2 and then square it.
((3/8)/2)^2=(3/8*1/2)^2=(3/16)^2=9/256(382)2=(38⋅12)2=(316)2=9256
Add this value to the left hand side
8(x^2+3/8x+9/256)=28(x2+38x+9256)=2
Add 8(9/256)8(9256) to the right hand side because of the factoring we did earlier.
8(x^2+3/8x+9/256)=2+8(9/256)8(x2+38x+9256)=2+8(9256)
You now have a perfect square trinomial
8(x+3/16)^2=2+8(9/256)8(x+316)2=2+8(9256)
Simplify
8(x+3/16)^2=2+cancel8(9/(cancel256 32))
Convert 2 to an improper fraction
8(x+3/16)^2=64/32+(9/(32))
Simplify
8(x+3/16)^2=73/32
y=8(x+3/16)^2-73/32
Vertex form
y=(x-h)^2+k where (h,k) is the vertex
Vertex (-3/16,-73/32)
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