Solve by completing the square

Question

-2y^2-44y-30=0
Write your answers as integers, proper or improper fractions in simplest form or decimals round to the nearest hundredth

Answer 1

Starting with the equation -2y^2 - 44y - 30 = 0, we can first divide all terms by -2 to simplify:

y^2 + 22y + 15 = 0

Now, we want to complete the square by adding and subtracting the square of half the coefficient of y:

y^2 + 22y + (22/2)^2 = -15 + (22/2)^2
y^2 + 22y + 121 = -15 + 121
y^2 + 22y + 121 = 106

Now we can rewrite the equation in completed square form:

(y + 11)^2 = 106

Taking the square root of both sides gives us:

y + 11 = ±√106

Finally, solving for y gives us two solutions:

y = -11 ± √106

So the solutions are y = -11 + √106 and y = -11 - √106.