Question

Factor then solve.
1.81 - 4x²=0
2. 4s² + 9 = 12s

Answer 1

`1.)\ \ \ 81 - 4x^2=0\\\\9^2-(2x)^2=0\ \ \ \ \ and\ \ \ \ \ a^2-b^2=(a-b)(a+b)\\\\(9-2x)(9+2x)=0\ \ \ \Leftrightarrow\ \ \ 9-2x=0\ \ \ or\ \ \ 9+2x=0 \\\\9-2x=0\ \ \ \Leftrightarrow\ \ \ -2x=-9\ \ \ \Leftrightarrow\ \ \ x=4.5\\\\9+2x=0 \ \ \ \Leftrightarrow\ \ \ 2x=-9\ \ \ \Leftrightarrow\ \ \ x=-4.5\\\\.......................................................................\\\\`


`2.)\ \ \ 4s^2+ 9 = 12s\\\\4s^2-12s+ 9 =0\\\\(2s)^2-2\cdot2s\cdot3+3^2=0\\\\(2s-3)^2=0\ \ \ \Leftrightarrow\ \ \ 2s-3=0\ \ \ \Leftrightarrow\ \ \ 2s=3\ \ \ \Leftrightarrow\ \ \ s=1.5`

Answer 2

`1.\\81-4x^2=0\\\\9^2-(2x)^2=0\\\\(9-2x)(9+2x)=0\iff9-2x=0\ \vee\ 9+2x=0\\\\-2x=-9\ \vee\ 2x=-9\\\\x=4.5\ \vee\ x=-4.5`

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`2.\\4s^2+9=12s\\\\4s^2-12s+9=0\\\\(2s)^2-2\cdot2s\cdot3+3^2=0\\\\(2s-3)^2=0\\\\(2s-3)(2s-3)=0\iff2s-3=0\\\\2s=3\\\\s=1.5`