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