Solve 4x^2-2yx+25=left(2x-5right)^2

$$4 { x }^{ 2 } -2yx+25= { \left(2x-5 \right) }^{ 2 }$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=10\end{matrix}\right.$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-5\right)^{2}.

$$4x^{2}-2yx+25=4x^{2}-20x+25$$

Subtract 4x^{2} from both sides.

$$4x^{2}-2yx+25-4x^{2}=-20x+25$$

Combine 4x^{2} and -4x^{2} to get 0.

$$-2yx+25=-20x+25$$

Add 20x to both sides.

$$-2yx+25+20x=25$$

Subtract 25 from both sides.

$$-2yx+20x=25-25$$

Subtract 25 from 25 to get 0.

$$-2yx+20x=0$$

Combine all terms containing x.

$$\left(-2y+20\right)x=0$$

The equation is in standard form.

$$\left(20-2y\right)x=0$$

Divide 0 by -2y+20.

$$x=0$$

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=10\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-5\right)^{2}.

$$4x^{2}-2yx+25=4x^{2}-20x+25$$

Subtract 4x^{2} from both sides.

$$-2yx+25=4x^{2}-20x+25-4x^{2}$$

Combine 4x^{2} and -4x^{2} to get 0.

$$-2yx+25=-20x+25$$

Subtract 25 from both sides.

$$-2yx=-20x+25-25$$

Subtract 25 from 25 to get 0.

$$-2yx=-20x$$

The equation is in standard form.

$$\left(-2x\right)y=-20x$$

Divide both sides by -2x.

$$\frac{\left(-2x\right)y}{-2x}=-\frac{20x}{-2x}$$

Dividing by -2x undoes the multiplication by -2x.

$$y=-\frac{20x}{-2x}$$

Divide -20x by -2x.

$$y=10$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=10\end{matrix}\right.$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-5\right)^{2}.

$$4x^{2}-2yx+25=4x^{2}-20x+25$$

Subtract 4x^{2} from both sides.

$$4x^{2}-2yx+25-4x^{2}=-20x+25$$

Combine 4x^{2} and -4x^{2} to get 0.

$$-2yx+25=-20x+25$$

Add 20x to both sides.

$$-2yx+25+20x=25$$

Subtract 25 from both sides.

$$-2yx+20x=25-25$$

Subtract 25 from 25 to get 0.

$$-2yx+20x=0$$

Combine all terms containing x.

$$\left(-2y+20\right)x=0$$

The equation is in standard form.

$$\left(20-2y\right)x=0$$

Divide 0 by -2y+20.

$$x=0$$

Solve for y

$$\left\{\begin{matrix}\\y=10\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-5\right)^{2}.

$$4x^{2}-2yx+25=4x^{2}-20x+25$$

Subtract 4x^{2} from both sides.

$$-2yx+25=4x^{2}-20x+25-4x^{2}$$

Combine 4x^{2} and -4x^{2} to get 0.

$$-2yx+25=-20x+25$$

Subtract 25 from both sides.

$$-2yx=-20x+25-25$$

Subtract 25 from 25 to get 0.

$$-2yx=-20x$$

The equation is in standard form.

$$\left(-2x\right)y=-20x$$

Divide both sides by -2x.

$$\frac{\left(-2x\right)y}{-2x}=-\frac{20x}{-2x}$$

Dividing by -2x undoes the multiplication by -2x.

$$y=-\frac{20x}{-2x}$$

Divide -20x by -2x.

$$y=10$$