Question

Solve the following quadratic equation by completing the square. Simplify the solutions and rationalize denominators, if necessary.

y^2+5y+11=0

Answer 1

Explanation:

y^2 + 5y + 11 = 0

To ,complete the square' , take 1/2 of the y coefficient (1/2 * 5 = 2.5 ) square it (6.25) and add it and subtract it from the equation

y^2 + 5y + 6.25 - 6.25 + 11 = 0 now you can reduce the left 3 terms

(y + 2.5)^2 - 6.25 + 11 = 0 Simplify

(y+2.5)^2 + 4.75 = 0

(y+2.5)^2 = - 4.75 sqrt both sides

y + 2.5 = +- i sqrt (4.75) and subtract 2.5 from both sides

y = - 2.5 +- i sqrt(4.75)

or y = - 5/2 + - i sqrt (19/4)

or y = - 5/2 +- i sqrt (19) / 2