Solve by completing the square
r^2+26r-11=0
write your answers as integers, proper or improper fractions in simplest form or decimals rounded to the nearest hundredth
To solve by completing the square, we first isolate the r terms:
r^2 + 26r - 11 = 0
r^2 + 26r = 11.
Next, we need to find the constant c that would complete the square. We take half of the coefficient of r (which is 13) and square it (which is 169). We then add this constant to both sides of the equation:
r^2 + 26r + 169 = 11 + 169
(r + 13)^2 = 180.
Taking the square root of both sides, we get:
r + 13 = ±√180
r + 13 = ±6√5
r = -13 ± 6√5.
Therefore, the solutions are:
r = -13 + 6√5 or r = -13 - 6√5.