Solve by completing the square
g^2-28g=-47
To solve by completing the square, we first move the constant term to the right side of the equation:
g^2 - 28g = -47
g^2 - 28g + (28/2)^2 = -47 + (28/2)^2
g^2 - 28g + 196 = -47 + 196
g^2 - 28g + 196 = 149
Now, we can rewrite the left side of the equation as a perfect square:
(g-14)^2 = 149
To solve for g, take square root of both sides:
g - 14 = ±√149
g = 14 ±√149
Therefore, the solutions are:
g = 14 + √149
or
g = 14 - √149