# Thread: Make Y the subject

1. ## Make Y the subject

2(y)^2 - 3y = x + 2

2. ## Re: Make Y the subject

You should recognize this as a Quadratic Equation and proceed. Completing the Square would be a nice, instructive method.

3. ## Re: Make Y the subject

Less instructive: use the quadratic formula to solve the equation $\displaystyle 2y^2- 3y- (x+ 2)= 0$/

4. ## Re: Make Y the subject

Less instructive yet(!): let k = x + 2; then: 2y^2 - 3y - k = 0

5. ## Re: Make Y the subject

2(Y)^2 - 3Y - K = 0 (K = X+2)

Y^2 - (3/2)Y - K/2 = 0

(Y - 3/4)(Y - 3/4) - K/2 - 9/16 = 0

(Y - 3/4)^2 - (K/2 + 9/16) = 0

(Y - 3/4)^2 = (K/2 + 9/16)

Y - 3/4 = sqrt(K/2 + 9/16)

Y = 3/4 + sqrt(K/2 + 9/16)

Y = 3/4 + sqrt((X + 2)/2 + 9/16)

Y = 3/4 + sqrt((8X + 16)/16 + 9/16)

Y = 3/4 + sqrt((8X + 16 + 9)/16)

Y = sqrt((8X + 25)/16)

Y = (3 +/- sqrt(8X + 25))/4

6. ## Re: Make Y the subject

Originally Posted by ajwright
2(Y)^2 - 3Y - K = 0 (K = X+2)

Y^2 - (3/2)Y - K/2 = 0

(Y - 3/4)(Y - 3/4) - K/2 - 9/16 = 0

(Y - 3/4)^2 - (K/2 + 9/16) = 0

(Y - 3/4)^2 = (K/2 + 9/16)

Y - 3/4 = +/- sqrt(K/2 + 9/16)

Y = 3/4 +/- sqrt(K/2 + 9/16)

Y = 3/4 +/- sqrt((X + 2)/2 + 9/16)

Y = 3/4 +/- sqrt((8X + 16)/16 + 9/16)

Y = 3/4 +/- sqrt((8X + 16 + 9)/16)

Y = 3/4 +/- sqrt((8X + 25)/16)

Y = (3 +/- sqrt(8X + 25))/4
You need to try very hard make sure every step of your working is correct. See the corrections in red. The final answer is correct though, well done.

7. ## Re: Make Y the subject

WHY do all that work? Never heard of the quadratic formula?

2y^2 - 3y - k = 0 , where k = x + 2

y = {-(-3) +/- SQRT[(-3)^2 - 4(2)(-k)]} / 4

y = [3 +/- SQRT(9 + 8k)] / 4
Substitute k = x + 2:
y = [3 +/- SQRT(9 + 8(x + 2))] / 4

y = [3 +/- SQRT(8x + 25)] / 4

Done!