Answer: x = √(((-F - 4)^2)/16 - 1/2) + (F + 4)/4 or x = (F + 4)/4 - √(((-F - 4)^2)/16 - 1/2)
Step-by-step explanation:
Solve for x:
F x = 2 x^2 - 4 x + 1
Subtract 2 x^2 - 4 x + 1 from both sides:
-2 x^2 + F x + 4 x - 1 = 0
Collect in terms of x:
-1 + x (F + 4) - 2 x^2 = 0
Divide both sides by -2:
1/2 + 1/2 x (-F - 4) + x^2 = 0
Subtract 1/2 from both sides:
1/2 x (-F - 4) + x^2 = -1/2
Add 1/16 (-F - 4)^2 to both sides:
1/16 (-F - 4)^2 + 1/2 x (-F - 4) + x^2 = 1/16 (-F - 4)^2 - 1/2
Write the left hand side as a square:
(1/4 (-F - 4) + x)^2 = 1/16 (-F - 4)^2 - 1/2
Take the square root of both sides:
1/4 (-F - 4) + x = √(1/16 (-F - 4)^2 - 1/2) or 1/4 (-F - 4) + x = -√(1/16 (-F - 4)^2 - 1/2)
Subtract 1/4 (-F - 4) from both sides:
x = √(((-F - 4)^2)/16 - 1/2) + (F + 4)/4 or 1/4 (-F - 4) + x = -√(1/16 (-F - 4)^2 - 1/2)
Subtract 1/4 (-F - 4) from both sides:
Answer: x = √(((-F - 4)^2)/16 - 1/2) + (F + 4)/4 or x = (F + 4)/4 - √(((-F - 4)^2)/16 - 1/2)
