Question

What is the solution of the equation (x - 5)2 +3(x-5)+9 = 0? Use u substitution and the quadratic formula to solve.​

Answer 1

x=
`(7+3i√(3) )/(2)` and
`(7-3i√(3) )/(2)`

Explanation:

(x - 5)^(2) +3(x-5)+9

(x - 5)^(2)= x2−10x+25

3(x-5)= 3x-15

x^2-10x+25+3x-15+9

x^2-7x+19=0

a=1 b=-7 c=19

use quadratic formula

`\frac{-b+\sqrt{b^(2) -4ac} }{2a}`

`\frac{-(-7)+\sqrt{-7^(2)-4(1)(19) } }{2}`

`\frac{7+\sqrt{49{}-4(19) } }{2}`

`\frac{7+\sqrt{49{}-76 } }{2}`

`\frac{7+\sqrt{-27{} } }{2}`

`√(-27) =3i√(3)`

`(7+3i√(3) )/(2)`