Question

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

Answer 1

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

$x= \frac{-b+-\sqrt{b^2-4ac} }{2a}$

a= 1  b = -12  and c= 59

$x= \frac{12+-\sqrt{(-12)^2-4(1)(59)}}{2(1)}$

$x= \frac{12+-\sqrt{92}}{2}$

$x= \frac{12+-2\sqrt{23}}{2}$

Divide the 12 and square root terms by 2

$x=6+-\sqrt{23}$

so $x=6+\sqrt{23}$    and    $x=6-\sqrt{23}$

Answer 2

Answer:

Solution for x:

$6+\sqrt{23}i$   and   $6-\sqrt{23}i$

Step-by-step explanation:

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

It is quadratic equation and to solve for x.

using quadratic formula:

$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

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

Put the values into the formula

$x=\dfrac{12\pm\sqrt{12^2-4\cdot 1\cdot -59}}{2(1)}$

$x=\dfrac{12\pm \sqrt{-92}}{2}$

As we know, $\sqrt{-1}=i$

$x=6\pm\sqrt{23}i$

Exact value of x : $6+\sqrt{23}i$   and   $6-\sqrt{23}i$