Solve for w over the real numbers:
(3 w^2)/4+(2 w)/3-1/3 = 2
Multiply both sides by 4/3:
w^2+(8 w)/9-4/9 = 8/3
Add 4/9 to both sides:
w^2+(8 w)/9 = 28/9
Add 16/81 to both sides:
w^2+(8 w)/9+16/81 = 268/81
Write the left hand side as a square:
(w+4/9)^2 = 268/81
Take the square root of both sides:
w+4/9 = (2 sqrt(67))/9 or w+4/9 = -(2 sqrt(67))/9
Subtract 4/9 from both sides:
w = (2 sqrt(67))/9-4/9 or w+4/9 = -(2 sqrt(67))/9
Subtract 4/9 from both sides:
Answer: |
| w = (2 sqrt(67))/9-4/9 or w = -4/9-(2 sqrt(67))/9
