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# Sqaure root of l(l-5)=6

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Sqaure root of l(l-5)=6

Aug 6, 2017

#1
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Is this your question?

$$\sqrt{l(l-5)}=6$$

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  .

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

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Aug 7, 2017