Answer
[tex]x=\frac{3+-\sqrt{53} }{2}[/tex]
Step-by-step explanation:
x² - 3x - 11 = 0
quadratic formula : [tex]\frac{-b+-\sqrt{b^2-4(a)(c)} }{2(a)}[/tex]
where the values of a b and c are derived from the equation
the equation given is written in quadratic form
ax² + bx + c = 0 , x² - 3x - 11 = 0
knowing this we can assign variables
a = 1 , b = - 3 and c = -11
we then plug in these values into the quadratic formula
recall formula [tex]\frac{-b+-\sqrt{b^2-4(a)(c)} }{2(a)}[/tex]
we know a = 1 , b = - 3 and c = -11
- plug in values -
[tex]\frac{-(-3)+-\sqrt{3^2-4(-11)(1)} }{2(1)}[/tex]
the two negative signs in front of the 3 cancel out and it changes to +3
[tex]\frac{3+-\sqrt{3^2-4(-11)(1)} }{2(1)}[/tex]
3² = 3 * 3 = 9
[tex]\frac{3+-\sqrt{9-4(-11)(1)} }{2(1)}[/tex]
( above under square root ) : -4 * -11 * 1 = 44
below : 2 * 1 = 2
[tex]\frac{3+-\sqrt{9+44} }{2}[/tex]
9 + 44 = 53
we're left with [tex]x=\frac{3+-\sqrt{53} }{2}[/tex]
and we are done!
