Answer:
x = 6 + 4.796i and x = 6 - 4.796i
Explanation:
For this problem, we will simply apply the quadratic formula to find the values of x. The quadratic formula is as follows:
x = [-b +/- sqrt(b^2 - 4ac)] / 2a
Using the formula let's find the values of x.
x^2 - 12x - 6 = -65
x^2 - 12x - 6 + 65 = -65 + 65
x^2 - 12x + 59 = 0
The coefficient of x^2 is a, the coefficient of x is b, and the constant 59 is c.
Hence, for our formula we have the following values:
a = 1
b = -12
c = 59
x = [-b +/- sqrt(b^2 - 4ac)] / 2a
x = [-(-12) +/- sqrt( (-12)^2 - 4(1)(59) ) ] / 2(1)
x = [ 12 +/- sqrt ( 144 - 236 ) ] / 2
x = [ 12 +/- sqrt ( -92 ) ] / 2
x = [ 12 +/- sqrt ( -4 * 23 ) ] / 2
x = [ 12 +/- 2i sqrt(23) ] / 2
x = 6 +/- i sqrt(23)
Hence from the formula, we have two possible values for x, both complex solutions. Note, i is an imaginary number.
x = 6 + i sqrt(23) and x = 6 - i sqrt(23)
x = 6 + 4.796i and x = 6 - 4.796i
Cheers.