Solve y= for x.

x = sqrt((2 y)/5 - 31/100) + 3/10 or x = 3/10 - sqrt((2 y)/5 - 31/100)

Step-by-step explanation by completing the square:

Solve for x:

y = 1/2 x (5 x - 3) + 1

y = 1/2 x (5 x - 3) + 1 is equivalent to 1/2 x (5 x - 3) + 1 = y:

1/2 x (5 x - 3) + 1 = y

Expand out terms of the left hand side:

(5 x^2)/2 - (3 x)/2 + 1 = y

Multiply both sides by 2/5:

x^2 - (3 x)/5 + 2/5 = (2 y)/5

Subtract 2/5 from both sides:

x^2 - (3 x)/5 = (2 y)/5 - 2/5

Add 9/100 to both sides:

x^2 - (3 x)/5 + 9/100 = (2 y)/5 - 31/100

Write the left hand side as a square:

(x - 3/10)^2 = (2 y)/5 - 31/100

Take the square root of both sides:

x - 3/10 = sqrt((2 y)/5 - 31/100) or x - 3/10 = -sqrt((2 y)/5 - 31/100)

Add 3/10 to both sides:

x = sqrt((2 y)/5 - 31/100) + 3/10 or x - 3/10 = -sqrt((2 y)/5 - 31/100)

Add 3/10 to both sides:

 x = sqrt((2 y)/5 - 31/100) + 3/10 or x = 3/10 - sqrt((2 y)/5 - 31/100)