Question

Which of the following is a solution of 3x2 = 7x - 3?

Answer 1

we have

`3x^(2)=7x-3`

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`3x^(2)-7x=-3`

Factor the leading coefficient

`3(x^(2)-(7/3)x)=-3`

Complete the square. Remember to balance the equation by adding the same constants to each side

`3(x^(2)-(7/3)x+(49/36))=-3+(49/12)`

`3(x^(2)-(7/3)x+(49/36))=(13/12)`

Rewrite as perfect squares

`3(x-(7/6))^(2)=(13/12)`

`(x-(7/6))^(2)=(13/36)`

square root both sides

`x-(7)/(6)=(+/-) \sqrt{(13)/(36)}`

`x-(7)/(6)=(+/-) (√(13))/(6)`

`x=(7)/(6)(+/-) (√(13))/(6)`

The solutions are

`x=(7)/(6)+(√(13))/(6)=(-7+√(13))/(6)`

`x=(7)/(6)-(√(13))/(6)=(-7-√(13))/(6)`

therefore

The answer is

`x=(7\pm√(13))/(6)`

Answer 2

3x^2 = 7x - 3
3x^2 - 7x = -3
x^2 - 7/3x = -1
x^2 - 7/3x + 49/36 = -1 + 49/36 = 13/36
(x - 7/6)^2 = 13/36
x - 7/6 = + or - sqrt(13)/6
x = 7/6 + or - sqrt(13)/6
x = (7 + or - sqrt(13))/6