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:

Option 2 -  $x=\frac{7\pm3\sqrt{3}i}{2}$

Step-by-step explanation:

Given : Equation $(x-5)^2+3(x-5)+9=0$

To find : What is the solution of the equation ?

Solution :

Using substitution method,

Let y=x-5

$y^2+3y+9=0$

Using quadratic formula, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Here, a=1, b=3 and c=9

$y=\frac{-3\pm\sqrt{3^2-4(1)(9)}}{2(1)}$

$y=\frac{-3\pm\sqrt{-27}}{2}$

$y=\frac{-3\pm3\sqrt{3}i}{2}$

Substitute back,

$x=\frac{-3\pm3\sqrt{3}i}{2}+5$

$x=\frac{-3\pm3\sqrt{3}i+10}{2}$

$x=\frac{7\pm3\sqrt{3}i}{2}$

Therefore, option 2 is correct.