+26367 what is x if
\(4 + \sqrt {x-4} = \sqrt {x+14}\) ?
\(\begin{array}{|rcll|} \hline 4 + \sqrt {x-4} &=& \sqrt {x+14} \quad &|\quad \text{square both sides} \\ (4 + \sqrt {x-4})^2 &=& x+14 \\ 16+2\cdot 4 \cdot \sqrt {x-4} + \not{x}-4 &=& \not{x}+14 \\ 16+8 \cdot \sqrt {x-4} -4 &=& 14 \quad &|\quad +4-16\\ 8 \cdot \sqrt {x-4} &=& 14 +4-16 \\ 8 \cdot \sqrt {x-4} &=& 2 \quad &|\quad :2 \\ 4 \cdot \sqrt {x-4} &=& 1 \quad &|\quad \text{square both sides} \\ 16 \cdot (x-4) &=& 1^2 \\ 16 \cdot (x-4) &=& 1 \\ 16x-64 &=& 1 \quad &|\quad +64 \\ 16x &=& 1+64 \\ 16x &=& 65 \quad &|\quad :16 \\ \mathbf{ x } & \mathbf{=} & \mathbf{\frac{65}{16} }\\ \hline \end{array}\)
+14929 what is x if 4 + sqrt (x-4) = sqrt (x+14)?
\(4+\sqrt{x-4}=\sqrt{x+14}\)
\(16+8\sqrt{x-4}+x-4=x+14\)
\(8\sqrt{x-4}=x+14-16+4-x\)
\(\sqrt{x-4}=\frac{2}{8}\)
\(x-4=\frac{1}{16}\)
\(x=4\ \frac{1}{16}\)
!
+26367 what is x if
\(4 + \sqrt {x-4} = \sqrt {x+14}\) ?
\(\begin{array}{|rcll|} \hline 4 + \sqrt {x-4} &=& \sqrt {x+14} \quad &|\quad \text{square both sides} \\ (4 + \sqrt {x-4})^2 &=& x+14 \\ 16+2\cdot 4 \cdot \sqrt {x-4} + \not{x}-4 &=& \not{x}+14 \\ 16+8 \cdot \sqrt {x-4} -4 &=& 14 \quad &|\quad +4-16\\ 8 \cdot \sqrt {x-4} &=& 14 +4-16 \\ 8 \cdot \sqrt {x-4} &=& 2 \quad &|\quad :2 \\ 4 \cdot \sqrt {x-4} &=& 1 \quad &|\quad \text{square both sides} \\ 16 \cdot (x-4) &=& 1^2 \\ 16 \cdot (x-4) &=& 1 \\ 16x-64 &=& 1 \quad &|\quad +64 \\ 16x &=& 1+64 \\ 16x &=& 65 \quad &|\quad :16 \\ \mathbf{ x } & \mathbf{=} & \mathbf{\frac{65}{16} }\\ \hline \end{array}\)
