Solve left(y-2right)^2/36-(x-3)/25=1

$$\frac{ { \left(y-2 \right) }^{ 2 } }{ 36 } - \frac{ (x-3) }{ 25 } = 1$$

Solve for x

$$x=\frac{25y^{2}}{36}-\frac{25y}{9}-\frac{173}{9}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 900, the least common multiple of 36,25.

$$25\left(y-2\right)^{2}-36\left(x-3\right)=900$$

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

$$25\left(y^{2}-4y+4\right)-36\left(x-3\right)=900$$

Use the distributive property to multiply 25 by y^{2}-4y+4.

$$25y^{2}-100y+100-36\left(x-3\right)=900$$

Use the distributive property to multiply -36 by x-3.

$$25y^{2}-100y+100-36x+108=900$$

Add 100 and 108 to get 208.

$$25y^{2}-100y+208-36x=900$$

Subtract 25y^{2} from both sides.

$$-100y+208-36x=900-25y^{2}$$

Add 100y to both sides.

$$208-36x=900-25y^{2}+100y$$

Subtract 208 from both sides.

$$-36x=900-25y^{2}+100y-208$$

Subtract 208 from 900 to get 692.

$$-36x=692-25y^{2}+100y$$

The equation is in standard form.

$$-36x=692+100y-25y^{2}$$

Divide both sides by -36.

$$\frac{-36x}{-36}=\frac{692+100y-25y^{2}}{-36}$$

Dividing by -36 undoes the multiplication by -36.

$$x=\frac{692+100y-25y^{2}}{-36}$$

Divide 692-25y^{2}+100y by -36.

$$x=\frac{25y^{2}}{36}-\frac{25y}{9}-\frac{173}{9}$$

Solve for y (complex solution)

$$y=-\frac{6\sqrt{x+22}}{5}+2$$

$$y=\frac{6\sqrt{x+22}}{5}+2$$

Solve for y

$$y=-\frac{6\sqrt{x+22}}{5}+2$$

$$y=\frac{6\sqrt{x+22}}{5}+2\text{, }x\geq -22$$