Is this correct now.
Problem #1
solve by completing the square.
2x^2+8x+3=0
My answer: x=-2 +/- sqrt (5)/(2)
Problem #2
solve by using the quadratic formula
5x^2+3x+1=0
My answer: No solution are defined.
You are not completing the square.
2x^2+8x+3=0
x^2 + 4x =- 3/2 now complete the square..
x^2 + 4x + 4 =- 3/2 + 4
(x+2)^2= ( sqrt (2.5))^2
x+2 = +- sqrt 2.5
to your answer above now.
isn't this the same answer as what i have
Yes, your answer is correct. The root of the equation 2x^2+8x+3=0 is indeed x = -2 +/- sqrt(5)/2. When solving quadratic equations using the completing the square method, you correctly completed the square by adding (4/2)^2 = 4 to both sides of the equation. This led you to the equation (x+2)^2 = sqrt(2.5)^2. Taking the square root of both sides and solving for x gives you x = -2 +/- sqrt(5)/2, which matches your initial answer.
Therefore, your solution for problem #1 is correct. Well done!