Solve by completing the square
2f^2+56f=-34
To solve by completing the square, first divide the equation by 2 to simplify:
f^2 + 28f = -17
Next, take half of the coefficient of f (28) and square it:
28/2 = 14
14^2 = 196
Add and subtract 196 inside the parentheses on the left side of the equation:
f^2 + 28f + 196 - 196 = -17
Now, rewrite the equation with a perfect square trinomial:
(f + 14)^2 - 196 = -17
Add 196 to both sides of the equation:
(f + 14)^2 = 179
Take the square root of both sides:
f + 14 = ± √179
Now, isolate f:
f = -14 ± √179