To solve by completing the square, we first move the constant term to the right side of the equation:
f^2 + 20f = 1
Next, we take half of the coefficient of f (which is 10) and square it to get the term we need to add and subtract to complete the square. So, we add (10)^2 = 100 to both sides:
f^2 + 20f + 100 = 101
Now we can rewrite the left side as a squared binomial:
(f + 10)^2 = 101
Taking the square root of both sides:
f + 10 = ±√101
f = -10 ± √101
So, the solutions are:
f = -10 + √101 or f = -10 - √101
These cannot be simplified any further, so the answers are:
f = -10 + √101 or f = -10 - √101
Solve by completing the square.
f^2 + 20f − 1 = 0
Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.
1 answer
1 answer