91Ó°ÊÓ

Complete the square to solve the quadratic equations by isolating$x^2$ andbx-terms.

role="math" localid="1647845514839" $$\begin{gathered} y^2−6y+2=0 \\ {y}^2−6y+2−2=0−2\text{ â¶Ä‰â¶Ä‰â¶Ä‰[ â¶Ä‰s³Ü²ú³Ù°ù²¹³¦³Ù â¶Ä‰}2\text{ â¶Ä‰f°ù´Ç³¾â€‰â¶Ä‰e²¹³¦³ó â¶Ä‰s¾±»å±ð â¶ÄÎë â¶Ä‰} \\ {y}^2−6y=−2\text{ â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰}[\text{ â¶Ä‰S¾±²Ô³¦±ð â¶Ä‰}{\left(\frac{−6}{2}\right)}^2=9\text{ â¶Ä‰},\text{ add â¶Ä‰}9\text{ â¶Ä‰to â¶Ä‰each â¶Ä‰side â¶Ä‰}] \\ {y}^2−6y+9=−2+9 \end{gathered}$$

The first factor$y^2−6y+9$, then take the square root of each side.

role="math" localid="1647845589501" $$\begin{gathered} y^2−6y+9=7 \\ {\left(y−3\right)}^2=7 \\ \sqrt{{\left(y−3\right)}^2}=Â\pm \sqrt{7} \\ y−3=Â\pm \sqrt{7} \end{gathered}$$

Now add 3 to both sides and separate the solutions.

$y−3+3=3Â\pm \sqrt{7}$

$$\begin{gathered} y=3Â\pm \sqrt{7} \\ y=3+\sqrt{7}\text{ â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â€‰or â¶Ä‰â€‰}y=3−\sqrt{7} \\ y=5.65\text{ â¶Ä‰â€‰â¶Ä‰or â¶Ä‰â€‰â¶Ä‰}y=0.35 \end{gathered}$$

Therefore, the solutions are 5.65 and 0.35.