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Serggg [28]
4 years ago
12

Solve for x over the complex numbers. x2+10x+41=0 Enter your answers in the boxes.

Mathematics
2 answers:
dimulka [17.4K]4 years ago
6 0

Answer:

x=-5-4i or x= -5+4i

tensa zangetsu [6.8K]4 years ago
4 0

<u>ANSWER</u>: x=-5-4i or x=-5+4i


<u>Explanation:</u>

The equation given to us is

x^2+10x+41=0.


One way to solve this equation is to use the quadratic formula;


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



When we compare x^2+10x+41=0 to the general quadratic equation ax^2+bx+c=0.


a=1,b=10,c=41


When we substitute these values in to the formula, we obtain;


x=\frac{-10\pm \sqrt{(-10)^2-4(1)(41)}}{2(1)}


We evaluate to obtain;


x=\frac{-10\pm \sqrt{100-164}}{2(1)}


x=\frac{-10\pm \sqrt{-64}}{2}


x=\frac{-10\pm \sqrt{64}\sqrt{-1}}{2}

Note that in complex numbers;

i=\sqrt{-1}


This implies that;

x=\frac{-10\pm 8i}{2}


x=-5\pm 4i


When we split the plus or minus sign we get;


x=-5-4i


or


x=-5+4i










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