How do you solve #4x - 2y^2 = 9#?

Question

Julia Adams · Accepted Answer

Without a system of equations, this problem will have infinite sollutions. You cna, however, isolate y to generate a function for the possible sollutions: #y=+-sqrt(2x-9/2)#

This is an equation ith two variables. Since it is not set in a system of equations, it can have infinite sollutions. However, not every sollution is possible. We must generate a function to determine the possible sollutions for this equation. In order to do that, we must isolate y. Follow these steps:

#2y^2=4x-9# #y^2=2x-9/2#

The square root is the operation opposite to the power. However, a square root has always two possible answers: one positive and the other negative. Apply the square root in both sides of the equation and the output will be:

#y=+-sqrt(2x-9/2)#

Isaiah Anthony · Answer

undefined To solve the equation 4x - 2y^2 = 9 for $ x $, first isolate $ x $ by moving the terms not containing $ x $ to the other side of the equation. Then, divide both sides by the coefficient of $ x $.

$$ 4x - 2y^2 = 9 $$

$$ 4x = 9 + 2y^2 $$

$$ x = \frac{9 + 2y^2}{4} $$

So, the solution for $ x $ is $ x = \frac{9 + 2y^2}{4} $.