Solve by completing the square.
s^2 − 14s = –29
Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.
To complete the square for the equation s^2 - 14s = -29, we need to add and subtract (14/2)^2 = 49 to the equation:
s^2 - 14s + 49 = -29 + 49
(s - 7)^2 = 20
Now, taking the square root of both sides, we get:
s - 7 = ±√20
s = 7 ± √20
Therefore, the solutions are:
s = 7 + √20
s = 7 - √20
These can also be written as decimals rounded to the nearest hundredth:
s ≈ 10.47
s ≈ 3.53