Solve y_{1}(5-x)^2/2=-2x^4

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

Solve for y_1

$$y_{1}=-\frac{4x^{4}}{\left(x-5\right)^{2}}$$

$$x\neq 5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$y_{1}\left(5-x\right)^{2}=-4x^{4}$$

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

$$y_{1}\left(25-10x+x^{2}\right)=-4x^{4}$$

Use the distributive property to multiply y_{1} by 25-10x+x^{2}.

$$25y_{1}-10y_{1}x+y_{1}x^{2}=-4x^{4}$$

Combine all terms containing y_{1}.

$$\left(25-10x+x^{2}\right)y_{1}=-4x^{4}$$

The equation is in standard form.

$$\left(x^{2}-10x+25\right)y_{1}=-4x^{4}$$

Divide both sides by 25-10x+x^{2}.

$$\frac{\left(x^{2}-10x+25\right)y_{1}}{x^{2}-10x+25}=-\frac{4x^{4}}{x^{2}-10x+25}$$

Dividing by 25-10x+x^{2} undoes the multiplication by 25-10x+x^{2}.

$$y_{1}=-\frac{4x^{4}}{x^{2}-10x+25}$$

Divide -4x^{4} by 25-10x+x^{2}.

$$y_{1}=-\frac{4x^{4}}{\left(x-5\right)^{2}}$$