Answer:
x=2±16i[tex]\sqrt{73}[/tex]
Step-by-step explanation:
1.) Using the PEMDAS distribute the [tex](x-2)^{2}[/tex] using the FOIL method
[tex](x-2)^2= x^2-4x+4[/tex]
2.) Distribute the -16 to ([tex](x-2)^2= x^2-4x+4[/tex])
[tex]-16(x^2-4x+4)= -16x^2+64x-64[/tex]
3.) Add the -25 to the equation
[tex](-16x^2+64x-64)-25=-16x^2+64x-89[/tex]=0
4.) Since this isn't factor-able, you must use the quadratic formula,
[tex]\frac{(-b (+ or -) \sqrt{(b^2-4ac)}}{2a}[/tex] and distrubute the numbers
a=-16 b=64 and c=-89
5.) Simplify the radical by finding the factors of -18688 that has a perfect root as one of the factors (which is -256 and 73).
[tex]\sqrt{-18688} =\sqrt{-256*73} =16i\sqrt{73}[/tex]
6.)Simplify the fraction
[tex]\frac{-64(+ or -)16i\sqrt{73} }{-32} ={2}(+ or -)16i\sqrt{73}[/tex]
7.) Your two roots are:
{2}(+ or -)16i\sqrt{73}
