Solve y=5(x-3)^2-217

$$y = 5 ( x - 3 ) ^ { 2 } - 217$$

Solve for y

$$y=5\left(x-3\right)^{2}-217$$

Solution Steps

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

$$y=5\left(x^{2}-6x+9\right)-217$$

Use the distributive property to multiply 5 by x^{2}-6x+9.

$$y=5x^{2}-30x+45-217$$

Subtract 217 from 45 to get -172.

$$y=5x^{2}-30x-172$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{5y+1085}}{5}+3$$

$$x=\frac{\sqrt{5y+1085}}{5}+3$$

Solve for x

$$x=-\frac{\sqrt{5y+1085}}{5}+3$$

$$x=\frac{\sqrt{5y+1085}}{5}+3\text{, }y\geq -217$$