Question

Solve for x in the equation ]x^{2} - 12x + 59 = 0

Answer 1

Solution for x:

`6+√(23)i` and
`6-√(23)i`

Explanation:

Given:
`x^2-12x+59=0`

It is quadratic equation and to solve for x.

using quadratic formula:

`x=(-b\pm√(b^2-4ac))/(2a)`

where, a=1, b=-12 and c=59

Put the values into the formula

`x=(12\pm√(12^2-4\cdot 1\cdot -59))/(2(1))`

`x=(12\pm √(-92))/(2)`

As we know,
`√(-1)=i`

`x=6\pm√(23)i`

Exact value of x :
`6+√(23)i` and
`6-√(23)i`

Answer 2

Step-by-step explanation:

`x^(2) - 12x + 59 = 0`

Given equaiton is in the form of ax^2 +bx+c=0

we apply quadratic formula to solve for x

`x= (-b+-√(b^2-4ac) )/(2a)`

a= 1 b = -12 and c= 59

`x= (12+-√((-12)^2-4(1)(59)))/(2(1))`

`x= (12+-√(92))/(2)`

`x= (12+-2√(23))/(2)`

Divide the 12 and square root terms by 2

`x=6+-√(23)`

so
`x=6+√(23)` and
`x=6-√(23)`