91Ó°ÊÓ

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

role="math" localid="1647845193301" $$\begin{gathered} y^2−8y+16=36 \\ {y}^2−8y+16−16=36−16\text{ â¶Ä‰â¶Ä‰â¶Ä‰[ â¶Ä‰s³Ü²ú³Ù°ù²¹³¦³Ù â¶Ä‰}16\text{ â¶Ä‰f°ù´Ç³¾â€‰â¶Ä‰e²¹³¦³ó â¶Ä‰s¾±»å±ð â¶ÄÎë â¶Ä‰} \\ {y}^2−8y+16=20+16\text{ â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰}[\text{ â¶Ä‰S¾±²Ô³¦±ð â¶Ä‰}{\left(\frac{8}{2}\right)}^2=16\text{ â¶Ä‰},\text{ add â¶Ä‰}16\text{ â¶Ä‰to â¶Ä‰each â¶Ä‰side â¶Ä‰}] \\ {y}^2−8y+16=36 \end{gathered}$$

The first factor $y^2−8y+16$, then take the square root of each side.

role="math" localid="1647845268333" $$\begin{gathered} y^2−8y+16=36 \\ {\left(y−4\right)}^2=36 \\ \sqrt{{\left(y−4\right)}^2}=Â\pm \sqrt{36} \\ y−4=Â\pm 6 \end{gathered}$$

Now add 4 to both sides and separate the solutions.

$y−4+4=4Â\pm 6$

$$\begin{gathered} y=4Â\pm 6 \\ y=4+6\text{ â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â€‰or â¶Ä‰â€‰}y=4−6 \\ y=10\text{ â¶Ä‰â€‰â¶Ä‰or â¶Ä‰â€‰â¶Ä‰}y=−2 \end{gathered}$$

Therefore, the solutions are 10 and -2.