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.

x = StartFraction negative 3 plus-or-minus 3 i StartRoot 3 EndRoot Over 2 EndFraction
x = StartFraction 7 plus-or-minus 3 i StartRoot 3 EndRoot Over 2 EndFraction
x = 2
x = 8

Answer 1

Option 2

Explanation:

I just took the test and got it right.

Answer 2

Option 2 -
`x=(7\pm3√(3)i)/(2)`

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=(-b\pm√(b^2-4ac))/(2a)`

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

`y=(-3\pm√(3^2-4(1)(9)))/(2(1))`

`y=(-3\pm√(-27))/(2)`

`y=(-3\pm3√(3)i)/(2)`

Substitute back,

`x=(-3\pm3√(3)i)/(2)+5`

`x=(-3\pm3√(3)i+10)/(2)`

`x=(7\pm3√(3)i)/(2)`

Therefore, option 2 is correct.