Question

Solve by completing the square.

k2 − 28k = –13

Answer 1

To solve for k using the method of completing the square, we want to rewrite the equation in the form (k - h)^2 = m, where h and m are constants.

First, let's move the constant term to the right side of the equation:

k^2 - 28k + 13 = 0

Next, we need to find the value to add and subtract in order to complete the square. To do this, we take half of the coefficient of the k term (-28/2 = -14) and square it (-14)^2 = 196. We add and subtract 196 inside the parentheses:

k^2 - 28k + 196 - 196 + 13 = 0

Now we can rewrite the quadratic as a square of a binomial:

(k - 14)^2 - 183 = 0

Next, let's move the constant term to the right side:

(k - 14)^2 = 183

Now, we solve for k by taking the square root of both sides:

k - 14 = ±sqrt(183)

To isolate k, we add 14 to both sides:

k = 14 ±sqrt(183)

Therefore, the solutions to the equation are k = 14 + sqrt(183) and k = 14 - sqrt(183).