Question

Find all complex solutions of X^2-5X -5= 0

Answer 1

Answer:

x =  [5 + 3√5]/2   or x =  [5  -3√5]/2

Step-by-step explanation:

Points to remember

Solution of a quadratic equation ax² + bx + c = 0

x = [-b ± √(b² - 4ac)]/2a

To find the solutions of given equation

It is given  x² - 5x - 5 = 0

here a = 1, b = -5 and c = -5

x = [-b ± √(b² - 4ac)]/2a

 =  [--5 ± √((-5)² - 4*1*-5)]/2*1

 = [5 ± √(25 + 20)]/2

 =  [5 ± √(45)]/2

 =  [5 ± 3√5]/2

x =  [5 + 3√5]/2   or x =  [5  -3√5]/2

Answer 2

ANSWER

$x = \frac{ 5 - 3\sqrt{ 5} }{2} \: or \: x = \frac{ 5 +3 \sqrt{ 5} }{2}$

EXPLANATION

The given equation is

${x}^{2} - 5x - 5 = 0$

The solution is given by the formula

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

where a=1, b=-5, c=-5

We substitute into the formula to get;

$x = \frac{ - - 5 \pm \sqrt{ {( - 5)}^{2} - 4(1)( - 5)} }{2(1)}$

We simplify to get,

$x = \frac{ 5 \pm \sqrt{ 45} }{2}$

The solutions are:

$x = \frac{ 5 - 3\sqrt{ 5} }{2} \: or \: x = \frac{ 5 +3 \sqrt{ 5} }{2}$

The equation has no complex roots.