Question

- 16(x - 2)² – 25=0​

Answer 1

x=2±16i
`√(73)`

Explanation:

1.) Using the PEMDAS distribute the
`(x-2)^(2)` using the FOIL method

`(x-2)^2= x^2-4x+4`

2.) Distribute the -16 to (
`(x-2)^2= x^2-4x+4`)

`-16(x^2-4x+4)= -16x^2+64x-64`

3.) Add the -25 to the equation

`(-16x^2+64x-64)-25=-16x^2+64x-89`=0

4.) Since this isn't factor-able, you must use the quadratic formula,

`((-b (+ or -) √((b^2-4ac)))/(2a)` 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).

`√(-18688) =√(-256*73) =16i√(73)`

6.)Simplify the fraction

`(-64(+ or -)16i√(73) )/(-32) ={2}(+ or -)16i√(73)`

7.) Your two roots are:

{2}(+ or -)16i\sqrt{73}