Question

Which of the following are solutions to the equation below?4x^2-12x+9=5

Answer 1

`x=(-√(5)+3)/(2)` and
`x=(√(5)+3)/(2)`

Explanation:

`4x^2-12x+9=5`

To solve for x we need to make right hand side 0

Subtract 5 on both sides

`4x^2-12x+4=0`

Divide whole equation by 4

`x^2-3x+1=0`

Apply quadratic formula to solve for x

`x=(-b+-√(b^2-4ac))/(2a)`

the value of a=1, b=-3 and c=1

`x=(-(-3)+-√((-3)^2-4(1)(1)))/(2(1))`

`x=(3+-√(5))/(2)`

`x=(-√(5)+3)/(2)` and
`x=(√(5)+3)/(2)`

Answer 2

`4x^2-12x+9=5\\4x^2-12x+9-5=0\\4x^2-12x+4=0 \ \ \ |:4\\x^2-3x+1=0 \\ \\ x= \cfrac{3б √((-3)^2-4) }{2}= \cfrac{3б √(9-4) }{2}= \cfrac{3б √(5) }{2}`

Correct answers are C and E