Solve y=20left(30-xright)^2/30^2+1

$$y = 20 \frac{ { \left( 30-x \right) }^{ 2 } }{ { 30 }^{ 2 } } +1$$

Solve for y

$$y=\frac{\left(30-x\right)^{2}+45}{45}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(30-x\right)^{2}.

$$y=20\times \frac{900-60x+x^{2}}{30^{2}}+1$$

Calculate 30 to the power of 2 and get 900.

$$y=20\times \frac{900-60x+x^{2}}{900}+1$$

Cancel out 900, the greatest common factor in 20 and 900.

$$y=\frac{900-60x+x^{2}}{45}+1$$

Divide each term of 900-60x+x^{2} by 45 to get 20-\frac{4}{3}x+\frac{1}{45}x^{2}.

$$y=20-\frac{4}{3}x+\frac{1}{45}x^{2}+1$$

Add 20 and 1 to get 21.

$$y=21-\frac{4}{3}x+\frac{1}{45}x^{2}$$

Solve for x (complex solution)

$$x=3\sqrt{5y-5}+30$$

$$x=-3\sqrt{5y-5}+30$$

Solve for x

$$x=3\sqrt{5y-5}+30$$

$$x=-3\sqrt{5y-5}+30\text{, }y\geq 1$$