Question

homework assignment 2.5 quadratic equations
due friday by 11:59pm points 15 submitting an external tool
homework assignment 2.5 quadratic equations
score: 8/15 answered: 8/15
question 9
solve the equation by completing the square: $y^{2}-2y + 19 = 3$
-1 + 15i,-1 - 15i
-15 - \sqrt{3}i,-15 + \sqrt{3}i
1 - \sqrt{15}i,1 + \sqrt{15}i
-1 - \sqrt{15}i,-1 + \sqrt{15}i
1 - 15i,1 + 15i
question help:

Explanation:

Step1: Rearrange the equation

First, move the constant term to the right - hand side: $y^{2}-2y=3 - 19$, so $y^{2}-2y=-16$.

Step2: Complete the square on the left - hand side

For the quadratic expression $y^{2}-2y$, the coefficient of $y$ is $-2$. Half of it is $-1$, and its square is $1$. Add $1$ to both sides of the equation: $y^{2}-2y + 1=-16 + 1$.
The left - hand side can be written as a perfect square: $(y - 1)^{2}=-15$.

Step3: Solve for $y$

Take the square root of both sides: $y-1=\pm\sqrt{-15}=\pm\sqrt{15}i$.
Then $y = 1\pm\sqrt{15}i$.

Answer:

C. $1-\sqrt{15}i,1+\sqrt{15}i$