Solve y=2*[(x-1)^2-36]

$$y = 2 \cdot [ ( x - 1 ) ^ { 2 } - 36 ]$$

Solve for y

$$y=2\left(x-7\right)\left(x+5\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

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

Subtract 36 from 1 to get -35.

$$y=2\left(x^{2}-2x-35\right)$$

Use the distributive property to multiply 2 by x^{2}-2x-35.

$$y=2x^{2}-4x-70$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{2y+144}}{2}+1$$

$$x=\frac{\sqrt{2y+144}}{2}+1$$

Solve for x

$$x=-\frac{\sqrt{2y+144}}{2}+1$$

$$x=\frac{\sqrt{2y+144}}{2}+1\text{, }y\geq -72$$