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

Question

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

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Ella 6 days 2021-10-13T06:00:02+00:00 2 Answers 0

Answers ( )

    0
    2021-10-13T06:01:02+00:00

    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.

    0
    2021-10-13T06:01:42+00:00

    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

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