Solve X=(x-4)^2-3

$$X = ( x - 4 ) ^ { 2 } - 3$$

Solve for X

$$X=\left(x-4\right)^{2}-3$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-4\right)^{2}.

$$X=x^{2}-8x+16-3$$

Subtract 3 from 16 to get 13.

$$X=x^{2}-8x+13$$

Solve for x (complex solution)

$$x=-\sqrt{X+3}+4$$

$$x=\sqrt{X+3}+4$$

Solve for x

$$x=-\sqrt{X+3}+4$$

$$x=\sqrt{X+3}+4\text{, }X\geq -3$$