Question

Solve quadratic equations of the form $x^2+bx+c=0$by completing the square.

In the following exercises , solve by completing the square.

$y^2-14=6y$

Short answer

The required value of$y$is$3+\sqrt{23},3-\sqrt{23}$

Step-by-step solution

Given information

$y^2-14=6y$

Calculation

$$\begin{gathered} y^2-14=6y \\ \Rightarrow y^2-6y=14 \\ \Rightarrow y^2-6y+(\frac{1}{2}\times {(-6))}^2=14+9 \\ \Rightarrow y^2-6y+9=14+9 \\ \Rightarrow {(y-3)}^2=23\Rightarrow y-3=\pm \sqrt{23} \\ \Rightarrow y=3\pm \sqrt{23} \\ =3+\sqrt{23},3-\sqrt{23} \end{gathered}$$

The required value of$y$is$3+\sqrt{23},3-\sqrt{23}$