Solve (x-1)^2+y/4=6

$$( x - 1 ) ^ { 2 } + \frac { y } { 4 } = 6$$

Solve for y

$$y=-4\left(x-1\right)^{2}+24$$

Solution Steps

Multiply both sides of the equation by 4.

$$4\left(x-1\right)^{2}+y=24$$

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

$$4\left(x^{2}-2x+1\right)+y=24$$

Use the distributive property to multiply 4 by x^{2}-2x+1.

$$4x^{2}-8x+4+y=24$$

Subtract 4x^{2} from both sides.

$$-8x+4+y=24-4x^{2}$$

Add 8x to both sides.

$$4+y=24-4x^{2}+8x$$

Subtract 4 from both sides.

$$y=24-4x^{2}+8x-4$$

Subtract 4 from 24 to get 20.

$$y=20-4x^{2}+8x$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{24-y}}{2}+1$$

$$x=\frac{\sqrt{24-y}}{2}+1$$

Solve for x

$$x=-\frac{\sqrt{24-y}}{2}+1$$

$$x=\frac{\sqrt{24-y}}{2}+1\text{, }y\leq 24$$