Solve (x-3)^2/5^4+y^1/4^1=1

$$\frac { ( x - 3 ) ^ { 2 } } { 5 ^ { 4 } } + \frac { y ^ { 1 } } { 4 ^ { 1 } } = 1$$

Solve for y

$$y=-\frac{4\left(x-28\right)\left(x+22\right)}{625}$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$\frac{x^{2}-6x+9}{5^{4}}+\frac{y^{1}}{4^{1}}=1$$

Calculate 5 to the power of 4 and get 625.

$$\frac{x^{2}-6x+9}{625}+\frac{y^{1}}{4^{1}}=1$$

Calculate y to the power of 1 and get y.

$$\frac{x^{2}-6x+9}{625}+\frac{y}{4^{1}}=1$$

Calculate 4 to the power of 1 and get 4.

$$\frac{x^{2}-6x+9}{625}+\frac{y}{4}=1$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 625 and 4 is 2500. Multiply \frac{x^{2}-6x+9}{625} times \frac{4}{4}. Multiply \frac{y}{4} times \frac{625}{625}.

$$\frac{4\left(x^{2}-6x+9\right)}{2500}+\frac{625y}{2500}=1$$

Since \frac{4\left(x^{2}-6x+9\right)}{2500} and \frac{625y}{2500} have the same denominator, add them by adding their numerators.

$$\frac{4\left(x^{2}-6x+9\right)+625y}{2500}=1$$

Do the multiplications in 4\left(x^{2}-6x+9\right)+625y.

$$\frac{4x^{2}-24x+36+625y}{2500}=1$$

Divide each term of 4x^{2}-24x+36+625y by 2500 to get \frac{1}{625}x^{2}-\frac{6}{625}x+\frac{9}{625}+\frac{1}{4}y.

$$\frac{1}{625}x^{2}-\frac{6}{625}x+\frac{9}{625}+\frac{1}{4}y=1$$

Subtract \frac{1}{625}x^{2} from both sides.

$$-\frac{6}{625}x+\frac{9}{625}+\frac{1}{4}y=1-\frac{1}{625}x^{2}$$

Add \frac{6}{625}x to both sides.

$$\frac{9}{625}+\frac{1}{4}y=1-\frac{1}{625}x^{2}+\frac{6}{625}x$$

Subtract \frac{9}{625} from both sides.

$$\frac{1}{4}y=1-\frac{1}{625}x^{2}+\frac{6}{625}x-\frac{9}{625}$$

Subtract \frac{9}{625} from 1 to get \frac{616}{625}.

$$\frac{1}{4}y=\frac{616}{625}-\frac{1}{625}x^{2}+\frac{6}{625}x$$

The equation is in standard form.

$$\frac{1}{4}y=\frac{616+6x-x^{2}}{625}$$

Multiply both sides by 4.

$$\frac{\frac{1}{4}y}{\frac{1}{4}}=-\frac{\frac{\left(x-28\right)\left(x+22\right)}{625}}{\frac{1}{4}}$$

Dividing by \frac{1}{4} undoes the multiplication by \frac{1}{4}.

$$y=-\frac{\frac{\left(x-28\right)\left(x+22\right)}{625}}{\frac{1}{4}}$$

Divide -\frac{\left(-28+x\right)\left(22+x\right)}{625} by \frac{1}{4} by multiplying -\frac{\left(-28+x\right)\left(22+x\right)}{625} by the reciprocal of \frac{1}{4}.

$$y=-\frac{4\left(x-28\right)\left(x+22\right)}{625}$$

Solve for x (complex solution)

$$x=-\frac{25\sqrt{4-y}}{2}+3$$

$$x=\frac{25\sqrt{4-y}}{2}+3$$

Solve for x

$$x=-\frac{25\sqrt{4-y}}{2}+3$$

$$x=\frac{25\sqrt{4-y}}{2}+3\text{, }y\leq 4$$