Solve 625/4x^2-10x^2=5625/64x^2-{left(125/8x-10xright)}^2

$$\frac{ 625 }{ 4 } { x }^{ 2 } -10 { x }^{ 2 } = \frac{ 5625 }{ 64 } { x }^{ 2 } - { \left( \frac{ 125 }{ 8 } x-10x \right) }^{ 2 }$$

Solve for x

$$x=0$$

Steps by Finding Square Root

Combine \frac{625}{4}x^{2} and -10x^{2} to get \frac{585}{4}x^{2}.

$$\frac{585}{4}x^{2}=\frac{5625}{64}x^{2}-\left(\frac{125}{8}x-10x\right)^{2}$$

Combine \frac{125}{8}x and -10x to get \frac{45}{8}x.

$$\frac{585}{4}x^{2}=\frac{5625}{64}x^{2}-\left(\frac{45}{8}x\right)^{2}$$

Expand \left(\frac{45}{8}x\right)^{2}.

$$\frac{585}{4}x^{2}=\frac{5625}{64}x^{2}-\left(\frac{45}{8}\right)^{2}x^{2}$$

Calculate \frac{45}{8} to the power of 2 and get \frac{2025}{64}.

$$\frac{585}{4}x^{2}=\frac{5625}{64}x^{2}-\frac{2025}{64}x^{2}$$

Combine \frac{5625}{64}x^{2} and -\frac{2025}{64}x^{2} to get \frac{225}{4}x^{2}.

$$\frac{585}{4}x^{2}=\frac{225}{4}x^{2}$$

Subtract \frac{225}{4}x^{2} from both sides.

$$\frac{585}{4}x^{2}-\frac{225}{4}x^{2}=0$$

Combine \frac{585}{4}x^{2} and -\frac{225}{4}x^{2} to get 90x^{2}.

$$90x^{2}=0$$

Divide both sides by 90. Zero divided by any non-zero number 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

Combine \frac{625}{4}x^{2} and -10x^{2} to get \frac{585}{4}x^{2}.

$$\frac{585}{4}x^{2}=\frac{5625}{64}x^{2}-\left(\frac{125}{8}x-10x\right)^{2}$$

Combine \frac{125}{8}x and -10x to get \frac{45}{8}x.

$$\frac{585}{4}x^{2}=\frac{5625}{64}x^{2}-\left(\frac{45}{8}x\right)^{2}$$

Expand \left(\frac{45}{8}x\right)^{2}.

$$\frac{585}{4}x^{2}=\frac{5625}{64}x^{2}-\left(\frac{45}{8}\right)^{2}x^{2}$$

Calculate \frac{45}{8} to the power of 2 and get \frac{2025}{64}.

$$\frac{585}{4}x^{2}=\frac{5625}{64}x^{2}-\frac{2025}{64}x^{2}$$

Combine \frac{5625}{64}x^{2} and -\frac{2025}{64}x^{2} to get \frac{225}{4}x^{2}.

$$\frac{585}{4}x^{2}=\frac{225}{4}x^{2}$$

Subtract \frac{225}{4}x^{2} from both sides.

$$\frac{585}{4}x^{2}-\frac{225}{4}x^{2}=0$$

Combine \frac{585}{4}x^{2} and -\frac{225}{4}x^{2} to get 90x^{2}.

$$90x^{2}=0$$

Divide both sides by 90. Zero divided by any non-zero number 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.

$$x=0$$