Solve by completing the square
2f^2+56f=-34
write your answer as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth
To solve this equation by completing the square, we want to rewrite it in the form \(a(f-h)^2+k\).
First, divide by 2 to make the coefficient of \(f^2\) 1:
\(f^2+28f=-17\)
Next, take half of the coefficient of \(f\), square it, and add it to both sides:
\(f^2+28f+196=-17+196\)
\(f^2+28f+196=179\)
Now, factor the left side:
\((f+14)^2=179\)
Take the square root of both sides:
\(f+14=\pm\sqrt{179}\)
Solve for \(f\):
\(f=-14\pm\sqrt{179}\)
Therefore, the solutions are:
\(f \approx -14 \pm 13.39\)
\(f \approx -27.39\) or \(f \approx -0.61\)