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

Answer:

x= $\frac{7+3i\sqrt{3} }{2}$ and $\frac{7-3i\sqrt{3} }{2}$

Step-by-step 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

$\frac{-b+\sqrt{b^{2} -4ac} }{2a}$

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

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

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

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

$\sqrt{-27} =3i\sqrt{3}$

$\frac{7+3i\sqrt{3} }{2}$