Solve 2*(x-1)^2=c-4x

$$2 \cdot ( x - 1 ) ^ { 2 } = c - 4 x$$

Solve for c

$$c=2\left(x^{2}+1\right)$$

Solution Steps

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

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

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

$$2x^{2}-4x+2=c-4x$$

Swap sides so that all variable terms are on the left hand side.

$$c-4x=2x^{2}-4x+2$$

Add 4x to both sides.

$$c=2x^{2}-4x+2+4x$$

Combine -4x and 4x to get 0.

$$c=2x^{2}+2$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{2\left(c-2\right)}}{2}$$

$$x=\frac{\sqrt{2\left(c-2\right)}}{2}$$

Solve for x

$$x=\frac{\sqrt{2\left(c-2\right)}}{2}$$

$$x=-\frac{\sqrt{2\left(c-2\right)}}{2}\text{, }c\geq 2$$