Answer:
x = sqrt(y/2 + 9/16) - 7/4 or x = -sqrt(y/2 + 9/16) - 7/4
Step-by-step explanation:
Solve for x:
y = 2 x^2 + 7 x + 5
y = 2 x^2 + 7 x + 5 is equivalent to 2 x^2 + 7 x + 5 = y:
2 x^2 + 7 x + 5 = y
Divide both sides by 2:
x^2 + (7 x)/2 + 5/2 = y/2
Subtract 5/2 from both sides:
x^2 + (7 x)/2 = y/2 - 5/2
Add 49/16 to both sides:
x^2 + (7 x)/2 + 49/16 = y/2 + 9/16
Write the left hand side as a square:
(x + 7/4)^2 = y/2 + 9/16
Take the square root of both sides:
x + 7/4 = sqrt(y/2 + 9/16) or x + 7/4 = -sqrt(y/2 + 9/16)
Subtract 7/4 from both sides:
x = sqrt(y/2 + 9/16) - 7/4 or x + 7/4 = -sqrt(y/2 + 9/16)
Subtract 7/4 from both sides:
Answer: x = sqrt(y/2 + 9/16) - 7/4 or x = -sqrt(y/2 + 9/16) - 7/4
