Solve x^2=3/20*0+5/20*1+5/20*4+4/20*9+frac{2}{10}*16+frac{1}{20}*25

$$x ^ { 2 } = \frac { 3 } { 20 } \cdot 0 + \frac { 5 } { 20 } \cdot 1 + \frac { 5 } { 20 } \cdot 4 + \frac { 4 } { 20 } \cdot 9 + \frac { 2 } { 10 } \cdot 16 + \frac { 1 } { 20 } \cdot 25$$

Solve for x

$$x = \frac{\sqrt{30}}{2} \approx 2.738612788$$

$$x = -\frac{\sqrt{30}}{2} \approx -2.738612788$$

Steps by Finding Square Root

Multiply \frac{3}{20} and 0 to get 0.

$$x^{2}=0+\frac{5}{20}\times 1+\frac{5}{20}\times 4+\frac{4}{20}\times 9+\frac{2}{10}\times 16+\frac{1}{20}\times 25$$

Reduce the fraction \frac{5}{20} to lowest terms by extracting and canceling out 5.

$$x^{2}=0+\frac{1}{4}\times 1+\frac{5}{20}\times 4+\frac{4}{20}\times 9+\frac{2}{10}\times 16+\frac{1}{20}\times 25$$

Multiply \frac{1}{4} and 1 to get \frac{1}{4}.

$$x^{2}=0+\frac{1}{4}+\frac{5}{20}\times 4+\frac{4}{20}\times 9+\frac{2}{10}\times 16+\frac{1}{20}\times 25$$

Add 0 and \frac{1}{4} to get \frac{1}{4}.

$$x^{2}=\frac{1}{4}+\frac{5}{20}\times 4+\frac{4}{20}\times 9+\frac{2}{10}\times 16+\frac{1}{20}\times 25$$

Reduce the fraction \frac{5}{20} to lowest terms by extracting and canceling out 5.

$$x^{2}=\frac{1}{4}+\frac{1}{4}\times 4+\frac{4}{20}\times 9+\frac{2}{10}\times 16+\frac{1}{20}\times 25$$

Multiply \frac{1}{4} and 4 to get 1.

$$x^{2}=\frac{1}{4}+1+\frac{4}{20}\times 9+\frac{2}{10}\times 16+\frac{1}{20}\times 25$$

Add \frac{1}{4} and 1 to get \frac{5}{4}.

$$x^{2}=\frac{5}{4}+\frac{4}{20}\times 9+\frac{2}{10}\times 16+\frac{1}{20}\times 25$$

Reduce the fraction \frac{4}{20} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{5}{4}+\frac{1}{5}\times 9+\frac{2}{10}\times 16+\frac{1}{20}\times 25$$

Multiply \frac{1}{5} and 9 to get \frac{9}{5}.

$$x^{2}=\frac{5}{4}+\frac{9}{5}+\frac{2}{10}\times 16+\frac{1}{20}\times 25$$

Add \frac{5}{4} and \frac{9}{5} to get \frac{61}{20}.

$$x^{2}=\frac{61}{20}+\frac{2}{10}\times 16+\frac{1}{20}\times 25$$

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{61}{20}+\frac{1}{5}\times 16+\frac{1}{20}\times 25$$

Multiply \frac{1}{5} and 16 to get \frac{16}{5}.

$$x^{2}=\frac{61}{20}+\frac{16}{5}+\frac{1}{20}\times 25$$

Add \frac{61}{20} and \frac{16}{5} to get \frac{25}{4}.

$$x^{2}=\frac{25}{4}+\frac{1}{20}\times 25$$

Multiply \frac{1}{20} and 25 to get \frac{5}{4}.

$$x^{2}=\frac{25}{4}+\frac{5}{4}$$

Add \frac{25}{4} and \frac{5}{4} to get \frac{15}{2}.

$$x^{2}=\frac{15}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{30}}{2} x=-\frac{\sqrt{30}}{2}$$

Steps Using the Quadratic Formula

Multiply \frac{3}{20} and 0 to get 0.

$$x^{2}=0+\frac{5}{20}\times 1+\frac{5}{20}\times 4+\frac{4}{20}\times 9+\frac{2}{10}\times 16+\frac{1}{20}\times 25$$

Reduce the fraction \frac{5}{20} to lowest terms by extracting and canceling out 5.

$$x^{2}=0+\frac{1}{4}\times 1+\frac{5}{20}\times 4+\frac{4}{20}\times 9+\frac{2}{10}\times 16+\frac{1}{20}\times 25$$

Multiply \frac{1}{4} and 1 to get \frac{1}{4}.

$$x^{2}=0+\frac{1}{4}+\frac{5}{20}\times 4+\frac{4}{20}\times 9+\frac{2}{10}\times 16+\frac{1}{20}\times 25$$

Add 0 and \frac{1}{4} to get \frac{1}{4}.

$$x^{2}=\frac{1}{4}+\frac{5}{20}\times 4+\frac{4}{20}\times 9+\frac{2}{10}\times 16+\frac{1}{20}\times 25$$

Reduce the fraction \frac{5}{20} to lowest terms by extracting and canceling out 5.

$$x^{2}=\frac{1}{4}+\frac{1}{4}\times 4+\frac{4}{20}\times 9+\frac{2}{10}\times 16+\frac{1}{20}\times 25$$

Multiply \frac{1}{4} and 4 to get 1.

$$x^{2}=\frac{1}{4}+1+\frac{4}{20}\times 9+\frac{2}{10}\times 16+\frac{1}{20}\times 25$$

Add \frac{1}{4} and 1 to get \frac{5}{4}.

$$x^{2}=\frac{5}{4}+\frac{4}{20}\times 9+\frac{2}{10}\times 16+\frac{1}{20}\times 25$$

Reduce the fraction \frac{4}{20} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{5}{4}+\frac{1}{5}\times 9+\frac{2}{10}\times 16+\frac{1}{20}\times 25$$

Multiply \frac{1}{5} and 9 to get \frac{9}{5}.

$$x^{2}=\frac{5}{4}+\frac{9}{5}+\frac{2}{10}\times 16+\frac{1}{20}\times 25$$

Add \frac{5}{4} and \frac{9}{5} to get \frac{61}{20}.

$$x^{2}=\frac{61}{20}+\frac{2}{10}\times 16+\frac{1}{20}\times 25$$

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{61}{20}+\frac{1}{5}\times 16+\frac{1}{20}\times 25$$

Multiply \frac{1}{5} and 16 to get \frac{16}{5}.

$$x^{2}=\frac{61}{20}+\frac{16}{5}+\frac{1}{20}\times 25$$

Add \frac{61}{20} and \frac{16}{5} to get \frac{25}{4}.

$$x^{2}=\frac{25}{4}+\frac{1}{20}\times 25$$

Multiply \frac{1}{20} and 25 to get \frac{5}{4}.

$$x^{2}=\frac{25}{4}+\frac{5}{4}$$

Add \frac{25}{4} and \frac{5}{4} to get \frac{15}{2}.

$$x^{2}=\frac{15}{2}$$

Subtract \frac{15}{2} from both sides.

$$x^{2}-\frac{15}{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{15}{2} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{15}{2}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{15}{2}\right)}}{2}$$

Multiply -4 times -\frac{15}{2}.

$$x=\frac{0±\sqrt{30}}{2}$$

Now solve the equation x=\frac{0±\sqrt{30}}{2} when ± is plus.

$$x=\frac{\sqrt{30}}{2}$$

Now solve the equation x=\frac{0±\sqrt{30}}{2} when ± is minus.

$$x=-\frac{\sqrt{30}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{30}}{2} x=-\frac{\sqrt{30}}{2}$$