Solve left(10-x-0.8yright)^2+left(0.6yright)^2=left(x+yright)^2

$${ \left(10-x-0.8y \right) }^{ 2 } + { \left(0.6y \right) }^{ 2 } = { \left(x+y \right) }^{ 2 }$$

Solve for x

$$x=\frac{10\left(25-4y\right)}{y+50}$$

$$y\neq -50$$

Steps for Solving Linear Equation

Square 10-x-0.8y.

$$x^{2}+1.6xy-20x+0.64y^{2}-16y+100+\left(0.6y\right)^{2}=\left(x+y\right)^{2}$$

Expand \left(0.6y\right)^{2}.

$$x^{2}+1.6xy-20x+0.64y^{2}-16y+100+0.6^{2}y^{2}=\left(x+y\right)^{2}$$

Calculate 0.6 to the power of 2 and get 0.36.

$$x^{2}+1.6xy-20x+0.64y^{2}-16y+100+0.36y^{2}=\left(x+y\right)^{2}$$

Combine 0.64y^{2} and 0.36y^{2} to get y^{2}.

$$x^{2}+1.6xy-20x+y^{2}-16y+100=\left(x+y\right)^{2}$$

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

$$x^{2}+1.6xy-20x+y^{2}-16y+100=x^{2}+2xy+y^{2}$$

Subtract x^{2} from both sides.

$$x^{2}+1.6xy-20x+y^{2}-16y+100-x^{2}=2xy+y^{2}$$

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

$$1.6xy-20x+y^{2}-16y+100=2xy+y^{2}$$

Subtract 2xy from both sides.

$$1.6xy-20x+y^{2}-16y+100-2xy=y^{2}$$

Combine 1.6xy and -2xy to get -0.4xy.

$$-0.4xy-20x+y^{2}-16y+100=y^{2}$$

Subtract y^{2} from both sides.

$$-0.4xy-20x-16y+100=y^{2}-y^{2}$$

Combine y^{2} and -y^{2} to get 0.

$$-0.4xy-20x-16y+100=0$$

Add 16y to both sides. Anything plus zero gives itself.

$$-0.4xy-20x+100=16y$$

Subtract 100 from both sides.

$$-0.4xy-20x=16y-100$$

Combine all terms containing x.

$$\left(-0.4y-20\right)x=16y-100$$

The equation is in standard form.

$$\left(-\frac{2y}{5}-20\right)x=16y-100$$

Divide both sides by -20-\frac{2}{5}y.

$$\frac{\left(-\frac{2y}{5}-20\right)x}{-\frac{2y}{5}-20}=\frac{16y-100}{-\frac{2y}{5}-20}$$

Dividing by -20-\frac{2}{5}y undoes the multiplication by -20-\frac{2}{5}y.

$$x=\frac{16y-100}{-\frac{2y}{5}-20}$$

Divide 16y-100 by -20-\frac{2}{5}y.

$$x=-\frac{10\left(4y-25\right)}{y+50}$$

Solve for y

$$y=\frac{50\left(5-x\right)}{x+40}$$

$$x\neq -40$$

Steps for Solving Linear Equation

Square 10-x-0.8y.

$$x^{2}+1.6xy-20x+0.64y^{2}-16y+100+\left(0.6y\right)^{2}=\left(x+y\right)^{2}$$

Expand \left(0.6y\right)^{2}.

$$x^{2}+1.6xy-20x+0.64y^{2}-16y+100+0.6^{2}y^{2}=\left(x+y\right)^{2}$$

Calculate 0.6 to the power of 2 and get 0.36.

$$x^{2}+1.6xy-20x+0.64y^{2}-16y+100+0.36y^{2}=\left(x+y\right)^{2}$$

Combine 0.64y^{2} and 0.36y^{2} to get y^{2}.

$$x^{2}+1.6xy-20x+y^{2}-16y+100=\left(x+y\right)^{2}$$

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

$$x^{2}+1.6xy-20x+y^{2}-16y+100=x^{2}+2xy+y^{2}$$

Subtract 2xy from both sides.

$$x^{2}+1.6xy-20x+y^{2}-16y+100-2xy=x^{2}+y^{2}$$

Combine 1.6xy and -2xy to get -0.4xy.

$$x^{2}-0.4xy-20x+y^{2}-16y+100=x^{2}+y^{2}$$

Subtract y^{2} from both sides.

$$x^{2}-0.4xy-20x+y^{2}-16y+100-y^{2}=x^{2}$$

Combine y^{2} and -y^{2} to get 0.

$$x^{2}-0.4xy-20x-16y+100=x^{2}$$

Subtract x^{2} from both sides.

$$-0.4xy-20x-16y+100=x^{2}-x^{2}$$

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

$$-0.4xy-20x-16y+100=0$$

Add 20x to both sides. Anything plus zero gives itself.

$$-0.4xy-16y+100=20x$$

Subtract 100 from both sides.

$$-0.4xy-16y=20x-100$$

Combine all terms containing y.

$$\left(-0.4x-16\right)y=20x-100$$

The equation is in standard form.

$$\left(-\frac{2x}{5}-16\right)y=20x-100$$

Divide both sides by -16-\frac{2}{5}x.

$$\frac{\left(-\frac{2x}{5}-16\right)y}{-\frac{2x}{5}-16}=\frac{20x-100}{-\frac{2x}{5}-16}$$

Dividing by -16-\frac{2}{5}x undoes the multiplication by -16-\frac{2}{5}x.

$$y=\frac{20x-100}{-\frac{2x}{5}-16}$$

Divide -100+20x by -16-\frac{2}{5}x.

$$y=-\frac{50\left(x-5\right)}{x+40}$$