[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: x = 7}}}}}}[/tex]
[tex]\sf \bf {\boxed {\mathbb {Step-by-step\:explanation:}}}[/tex]
[tex] \: ({x - 3})^{2} = 16[/tex]
➺[tex] \: (x - 3) = \sqrt{16} [/tex]
➺[tex] \: (x - 3) = \sqrt{4 \times 4} [/tex]
➺[tex] \: (x - 3) = \sqrt{( {4})^{2} } [/tex]
➺[tex] \: (x - 3) = ±4[/tex]
When [tex]x\:=\:+4[/tex], we have
➺[tex] \: x = 4 + 3[/tex]
➺[tex]\boxed{x\:=\:7}[/tex]
When [tex]x\:=\:-4[/tex], we have
➺ [tex]\:(x - 3) = - 4[/tex]
➺[tex] \: x = - 4 + 3[/tex]
➺ [tex]\boxed{x\:=\:-1}[/tex]
Therefore, the two values of [tex]x[/tex] are 7 and -1.
Hence, 7 is the positive value of [tex]x[/tex].
[tex]\sf \bf {\boxed {\mathbb {To\:verify:}}}[/tex]
➼[tex] \: ( {x - 3})^{2} = 16[/tex]
When [tex]x\:=\:7[/tex]
➼[tex] \: ({7 - 3)}^{2} = 16[/tex]
➼[tex] \: {4}^{2} = 16[/tex]
➼[tex] \: 16 = 16[/tex]
➼[tex] \: L.H.S.=R. H. S[/tex]
When [tex]x\:=\:-1[/tex]
[tex] \: ({x - 3})^{2} = 16[/tex]
➼[tex] \:( { - 1 - 3})^{2} = 16[/tex]
➼[tex]\: ({ - 4})^{2} = 16[/tex]
➼[tex] \: 16 = 16 [/tex]
➼[tex] \: L.H.S.=R. H. S[/tex]
[tex]\sf\purple{Hence\:verified. }[/tex] ✔
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{☂}}}}}[/tex]
