What is Y = 2x^2 + 7x + 5

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