Question

How can I isolate x in y=6x-2x²

Answer 1

Answer:

x = 3/2 ± √(9/4 − 1/2 y)

Step-by-step explanation:

y = 6x − 2x²

First, factor out the leading coefficient:

y = -2 (x² − 3x)

Complete the square.

y = -2 (x² − 3x + 9/4 − 9/4)

y = -2 (x² − 3x + 9/4) + 9/2

y = -2 (x − 3/2)² + 9/2

Solve for x.

-1/2 y = (x − 3/2)² − 9/4

9/4 − 1/2 y = (x − 3/2)²

±√(9/4 − 1/2 y) = x − 3/2

x = 3/2 ± √(9/4 − 1/2 y)