Solve 9x^2=0.36x^2+{left(2sqrt{34}div10right)}^2x^2

$$9 { x }^{ 2 } =0.36 { x }^{ 2 } + { \left(2 \sqrt{ 34 } \div 10 \right) }^{ 2 } { x }^{ 2 }$$

Solve for x

$$x=0$$

Steps by Finding Square Root

Divide 2\sqrt{34} by 10 to get \frac{1}{5}\sqrt{34}.

$$9x^{2}=0.36x^{2}+\left(\frac{1}{5}\sqrt{34}\right)^{2}x^{2}$$

Expand \left(\frac{1}{5}\sqrt{34}\right)^{2}.

$$9x^{2}=0.36x^{2}+\left(\frac{1}{5}\right)^{2}\left(\sqrt{34}\right)^{2}x^{2}$$

Calculate \frac{1}{5} to the power of 2 and get \frac{1}{25}.

$$9x^{2}=0.36x^{2}+\frac{1}{25}\left(\sqrt{34}\right)^{2}x^{2}$$

The square of \sqrt{34} is 34.

$$9x^{2}=0.36x^{2}+\frac{1}{25}\times 34x^{2}$$

Multiply \frac{1}{25} and 34 to get \frac{34}{25}.

$$9x^{2}=0.36x^{2}+\frac{34}{25}x^{2}$$

Combine 0.36x^{2} and \frac{34}{25}x^{2} to get \frac{43}{25}x^{2}.

$$9x^{2}=\frac{43}{25}x^{2}$$

Subtract \frac{43}{25}x^{2} from both sides.

$$9x^{2}-\frac{43}{25}x^{2}=0$$

Combine 9x^{2} and -\frac{43}{25}x^{2} to get \frac{182}{25}x^{2}.

$$\frac{182}{25}x^{2}=0$$

Multiply both sides by \frac{25}{182}, the reciprocal of \frac{182}{25}. Anything times zero gives zero.

$$x^{2}=0$$

Take the square root of both sides of the equation.

$$x=0 x=0$$

The equation is now solved. Solutions are the same.

$$x=0$$

Steps Using the Quadratic Formula

Divide 2\sqrt{34} by 10 to get \frac{1}{5}\sqrt{34}.

$$9x^{2}=0.36x^{2}+\left(\frac{1}{5}\sqrt{34}\right)^{2}x^{2}$$

Expand \left(\frac{1}{5}\sqrt{34}\right)^{2}.

$$9x^{2}=0.36x^{2}+\left(\frac{1}{5}\right)^{2}\left(\sqrt{34}\right)^{2}x^{2}$$

Calculate \frac{1}{5} to the power of 2 and get \frac{1}{25}.

$$9x^{2}=0.36x^{2}+\frac{1}{25}\left(\sqrt{34}\right)^{2}x^{2}$$

The square of \sqrt{34} is 34.

$$9x^{2}=0.36x^{2}+\frac{1}{25}\times 34x^{2}$$

Multiply \frac{1}{25} and 34 to get \frac{34}{25}.

$$9x^{2}=0.36x^{2}+\frac{34}{25}x^{2}$$

Combine 0.36x^{2} and \frac{34}{25}x^{2} to get \frac{43}{25}x^{2}.

$$9x^{2}=\frac{43}{25}x^{2}$$

Subtract \frac{43}{25}x^{2} from both sides.

$$9x^{2}-\frac{43}{25}x^{2}=0$$

Combine 9x^{2} and -\frac{43}{25}x^{2} to get \frac{182}{25}x^{2}.

$$\frac{182}{25}x^{2}=0$$

Multiply both sides by \frac{25}{182}, the reciprocal of \frac{182}{25}. Anything times zero gives zero.

$$x^{2}=0$$

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

$$x=\frac{0±\sqrt{0^{2}}}{2}$$

Take the square root of 0^{2}.

$$x=\frac{0±0}{2}$$

Divide 0 by 2.

$$x=0$$