Solve by completing the square.
v^2 − 30v = –7
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 need to rearrange the equation to isolate the variable on one side:
v^2 - 30v = -7
v^2 - 30v + 225 = -7 + 225
(v - 15)^2 = 218
Now we have a perfect square trinomial on the left side. Taking the square root of both sides, we get:
v - 15 = ±√218
v = 15 ± √218
So the solutions are:
v = 15 + √218
v = 15 - √218
These answers cannot be simplified further.