Question

Solve this quadratic equation using the quadratic formula. x^2 - 6x + 6 = 0

Answer 1

Explanation:

x= 6± √(6)^2-4(1)(6) /2(1)

=6± √12 /2

=6± 2√3 /2

=3± √3

Answer 2

Answer: The required solution of the given quadratic equation is

x = 3 + √3 and x = 3 - √3.

Step-by-step explanation: We are given to solve the following quadratic equation using quadratic formula :

`x^2-6x+6=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

Quadratic formula : The solution of a quadratic equation of the form
`ax^2+bx+c=0,~a\\eq 0` is given by

`x=(-b\pm√(b^2-4ac))/(2a)`

For the given quadratic equation (i), we have

a = 1, b = -6 and c = 6.

Therefore, the solution of equation (i) is given by

`x\\\\\\=(-b\pm√(b^2-4ac))/(2a)\\\\\\=(-(-6)\pm√((-6)^2-4* 1*6))/(2*1)\\\\\\=(6\pm√(36-24))/(2)\\\\\\=(6\pm√(12))/(2)\\\\\\=(6\pm2√(3))/(2)\\\\=3\pm\sqrt3.`.

Thus, the required solution of the given quadratic equation is

x = 3 + √3 and x = 3 - √3.