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Sqaure root of l(l-5)=6

Guest Aug 6, 2017
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\(\sqrt{l(l-5)}=6\)

                                                   Square both sides of the equation.

\(\sqrt{l(l-5)}^2=6^2 \\~\\ l(l-5)=36\)

                                                   Distribute the  l  to both terms in parenthesees.

\(l^2-5l=36\)

                                                   Subtract  36  from both sides of the equation.

\(l^2-5l-36=0\)

                                                   Use the quadratic formula to solve for  l  .

\(l=\frac{-(-5)\pm\sqrt{(-5)^2-4(1)(-36)}}{2(1)} \\~\\ l=\frac{5\pm\sqrt{25+144}}{2} \\~\\ l=\frac{5\pm13}{2} \\~\\ \begin{array} \ l=\frac{5+13}{2}\qquad &\text{or}&\qquad l=\frac{5-13}{2}\\~\\ l=9&\text{or}&\qquad l=-4 \end{array}\)

hectictar  Aug 7, 2017

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