Solve {l}{[21/33+22/33+23/33+24/33+frac{25}{33}+frac{26}{33}+frac{27}{33}+frac{28}{33}+frac{29}{33}+frac{30}{33}]=mpim=?}{{llll}{text{1)}frac{245}{33}}&{text{2)}frac{250}{33}}&{text{3)}frac{235}{33}}&{text{4)}7frac{24}{33}}}

$$\left. \begin{array} { l } { [ \frac { 21 } { 33 } + \frac { 22 } { 33 } + \frac { 23 } { 33 } + \frac { 24 } { 33 } + \frac { 25 } { 33 } + \frac { 26 } { 33 } + \frac { 27 } { 33 } + \frac { 28 } { 33 } + \frac { 29 } { 33 } + \frac { 30 } { 33 } ] = m \pi m = ? } \\ { \left. \begin{array} { l l l l } { \text { 1) } \frac { 245 } { 33 } } & { \text { 2) } \frac { 250 } { 33 } } & { \text { 3) } \frac { 235 } { 33 } } & { \text { 4) } 7 \frac { 24 } { 33 } } \end{array} \right. } \end{array} \right.$$

Solve for m

$$m = \frac{\sqrt{\frac{935}{\pi}}}{11} \approx 1.56833265$$

$$m = -\frac{\sqrt{\frac{935}{\pi}}}{11} \approx -1.56833265$$

Steps by Finding Square Root

Multiply m and m to get m^{2}.

$$\frac{21}{33}+\frac{22}{33}+\frac{23}{33}+\frac{24}{33}+\frac{25}{33}+\frac{26}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Since \frac{21}{33} and \frac{22}{33} have the same denominator, add them by adding their numerators.

$$\frac{21+22}{33}+\frac{23}{33}+\frac{24}{33}+\frac{25}{33}+\frac{26}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Add 21 and 22 to get 43.

$$\frac{43}{33}+\frac{23}{33}+\frac{24}{33}+\frac{25}{33}+\frac{26}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Since \frac{43}{33} and \frac{23}{33} have the same denominator, add them by adding their numerators.

$$\frac{43+23}{33}+\frac{24}{33}+\frac{25}{33}+\frac{26}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Add 43 and 23 to get 66.

$$\frac{66}{33}+\frac{24}{33}+\frac{25}{33}+\frac{26}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Divide 66 by 33 to get 2.

$$2+\frac{24}{33}+\frac{25}{33}+\frac{26}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Reduce the fraction \frac{24}{33} to lowest terms by extracting and canceling out 3.

$$2+\frac{8}{11}+\frac{25}{33}+\frac{26}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Convert 2 to fraction \frac{22}{11}.

$$\frac{22}{11}+\frac{8}{11}+\frac{25}{33}+\frac{26}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Since \frac{22}{11} and \frac{8}{11} have the same denominator, add them by adding their numerators.

$$\frac{22+8}{11}+\frac{25}{33}+\frac{26}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Add 22 and 8 to get 30.

$$\frac{30}{11}+\frac{25}{33}+\frac{26}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Least common multiple of 11 and 33 is 33. Convert \frac{30}{11} and \frac{25}{33} to fractions with denominator 33.

$$\frac{90}{33}+\frac{25}{33}+\frac{26}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Since \frac{90}{33} and \frac{25}{33} have the same denominator, add them by adding their numerators.

$$\frac{90+25}{33}+\frac{26}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Add 90 and 25 to get 115.

$$\frac{115}{33}+\frac{26}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Since \frac{115}{33} and \frac{26}{33} have the same denominator, add them by adding their numerators.

$$\frac{115+26}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Add 115 and 26 to get 141.

$$\frac{141}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Reduce the fraction \frac{141}{33} to lowest terms by extracting and canceling out 3.

$$\frac{47}{11}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Reduce the fraction \frac{27}{33} to lowest terms by extracting and canceling out 3.

$$\frac{47}{11}+\frac{9}{11}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Since \frac{47}{11} and \frac{9}{11} have the same denominator, add them by adding their numerators.

$$\frac{47+9}{11}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Add 47 and 9 to get 56.

$$\frac{56}{11}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Least common multiple of 11 and 33 is 33. Convert \frac{56}{11} and \frac{28}{33} to fractions with denominator 33.

$$\frac{168}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Since \frac{168}{33} and \frac{28}{33} have the same denominator, add them by adding their numerators.

$$\frac{168+28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Add 168 and 28 to get 196.

$$\frac{196}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Since \frac{196}{33} and \frac{29}{33} have the same denominator, add them by adding their numerators.

$$\frac{196+29}{33}+\frac{30}{33}=m^{2}\pi$$

Add 196 and 29 to get 225.

$$\frac{225}{33}+\frac{30}{33}=m^{2}\pi$$

Reduce the fraction \frac{225}{33} to lowest terms by extracting and canceling out 3.

$$\frac{75}{11}+\frac{30}{33}=m^{2}\pi$$

Reduce the fraction \frac{30}{33} to lowest terms by extracting and canceling out 3.

$$\frac{75}{11}+\frac{10}{11}=m^{2}\pi$$

Since \frac{75}{11} and \frac{10}{11} have the same denominator, add them by adding their numerators.

$$\frac{75+10}{11}=m^{2}\pi$$

Add 75 and 10 to get 85.

$$\frac{85}{11}=m^{2}\pi$$

Swap sides so that all variable terms are on the left hand side.

$$m^{2}\pi =\frac{85}{11}$$

Divide both sides by \pi .

$$\frac{\pi m^{2}}{\pi }=\frac{\frac{85}{11}}{\pi }$$

Dividing by \pi undoes the multiplication by \pi .

$$m^{2}=\frac{\frac{85}{11}}{\pi }$$

Divide \frac{85}{11} by \pi .

$$m^{2}=\frac{85}{11\pi }$$

Take the square root of both sides of the equation.

$$m=\frac{85}{\sqrt{935\pi }} m=-\frac{85}{\sqrt{935\pi }}$$

Steps Using the Quadratic Formula

Multiply m and m to get m^{2}.

$$\frac{21}{33}+\frac{22}{33}+\frac{23}{33}+\frac{24}{33}+\frac{25}{33}+\frac{26}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Since \frac{21}{33} and \frac{22}{33} have the same denominator, add them by adding their numerators.

$$\frac{21+22}{33}+\frac{23}{33}+\frac{24}{33}+\frac{25}{33}+\frac{26}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Add 21 and 22 to get 43.

$$\frac{43}{33}+\frac{23}{33}+\frac{24}{33}+\frac{25}{33}+\frac{26}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Since \frac{43}{33} and \frac{23}{33} have the same denominator, add them by adding their numerators.

$$\frac{43+23}{33}+\frac{24}{33}+\frac{25}{33}+\frac{26}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Add 43 and 23 to get 66.

$$\frac{66}{33}+\frac{24}{33}+\frac{25}{33}+\frac{26}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Divide 66 by 33 to get 2.

$$2+\frac{24}{33}+\frac{25}{33}+\frac{26}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Reduce the fraction \frac{24}{33} to lowest terms by extracting and canceling out 3.

$$2+\frac{8}{11}+\frac{25}{33}+\frac{26}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Convert 2 to fraction \frac{22}{11}.

$$\frac{22}{11}+\frac{8}{11}+\frac{25}{33}+\frac{26}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Since \frac{22}{11} and \frac{8}{11} have the same denominator, add them by adding their numerators.

$$\frac{22+8}{11}+\frac{25}{33}+\frac{26}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Add 22 and 8 to get 30.

$$\frac{30}{11}+\frac{25}{33}+\frac{26}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Least common multiple of 11 and 33 is 33. Convert \frac{30}{11} and \frac{25}{33} to fractions with denominator 33.

$$\frac{90}{33}+\frac{25}{33}+\frac{26}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Since \frac{90}{33} and \frac{25}{33} have the same denominator, add them by adding their numerators.

$$\frac{90+25}{33}+\frac{26}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Add 90 and 25 to get 115.

$$\frac{115}{33}+\frac{26}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Since \frac{115}{33} and \frac{26}{33} have the same denominator, add them by adding their numerators.

$$\frac{115+26}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Add 115 and 26 to get 141.

$$\frac{141}{33}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Reduce the fraction \frac{141}{33} to lowest terms by extracting and canceling out 3.

$$\frac{47}{11}+\frac{27}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Reduce the fraction \frac{27}{33} to lowest terms by extracting and canceling out 3.

$$\frac{47}{11}+\frac{9}{11}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Since \frac{47}{11} and \frac{9}{11} have the same denominator, add them by adding their numerators.

$$\frac{47+9}{11}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Add 47 and 9 to get 56.

$$\frac{56}{11}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Least common multiple of 11 and 33 is 33. Convert \frac{56}{11} and \frac{28}{33} to fractions with denominator 33.

$$\frac{168}{33}+\frac{28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Since \frac{168}{33} and \frac{28}{33} have the same denominator, add them by adding their numerators.

$$\frac{168+28}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Add 168 and 28 to get 196.

$$\frac{196}{33}+\frac{29}{33}+\frac{30}{33}=m^{2}\pi$$

Since \frac{196}{33} and \frac{29}{33} have the same denominator, add them by adding their numerators.

$$\frac{196+29}{33}+\frac{30}{33}=m^{2}\pi$$

Add 196 and 29 to get 225.

$$\frac{225}{33}+\frac{30}{33}=m^{2}\pi$$

Reduce the fraction \frac{225}{33} to lowest terms by extracting and canceling out 3.

$$\frac{75}{11}+\frac{30}{33}=m^{2}\pi$$

Reduce the fraction \frac{30}{33} to lowest terms by extracting and canceling out 3.

$$\frac{75}{11}+\frac{10}{11}=m^{2}\pi$$

Since \frac{75}{11} and \frac{10}{11} have the same denominator, add them by adding their numerators.

$$\frac{75+10}{11}=m^{2}\pi$$

Add 75 and 10 to get 85.

$$\frac{85}{11}=m^{2}\pi$$

Swap sides so that all variable terms are on the left hand side.

$$m^{2}\pi =\frac{85}{11}$$

Subtract \frac{85}{11} from both sides.

$$m^{2}\pi -\frac{85}{11}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$\pi m^{2}-\frac{85}{11}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \pi for a, 0 for b, and -\frac{85}{11} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{0±\sqrt{0^{2}-4\pi \left(-\frac{85}{11}\right)}}{2\pi }$$

Square 0.

$$m=\frac{0±\sqrt{-4\pi \left(-\frac{85}{11}\right)}}{2\pi }$$

Multiply -4 times \pi .

$$m=\frac{0±\sqrt{\left(-4\pi \right)\left(-\frac{85}{11}\right)}}{2\pi }$$

Multiply -4\pi times -\frac{85}{11}.

$$m=\frac{0±\sqrt{\frac{340\pi }{11}}}{2\pi }$$

Take the square root of \frac{340\pi }{11}.

$$m=\frac{0±\frac{2\sqrt{935\pi }}{11}}{2\pi }$$

Now solve the equation m=\frac{0±\frac{2\sqrt{935\pi }}{11}}{2\pi } when ± is plus.

$$m=\frac{85}{\sqrt{935\pi }}$$

Now solve the equation m=\frac{0±\frac{2\sqrt{935\pi }}{11}}{2\pi } when ± is minus.

$$m=-\frac{85}{\sqrt{935\pi }}$$

The equation is now solved.

$$m=\frac{85}{\sqrt{935\pi }} m=-\frac{85}{\sqrt{935\pi }}$$