Either 2i or -2i, when squared equal -4.
x2 +x=3x-5 so x2 -2x+5=0 which does not factor ( over the real numbers) so you can either complete the square of use the quadratic equation to solve. Let's complete the square. (x-1)2 =-4 x-1= plus of minus 2i so x=1+2i or x=1-2i Now check it just as you would a real answer. 1+2i -1 is 2i and 2i squared is -4 as desired Now 1-2i-1 is -2i and (-2i) squared is -4 also. We know the answer is not real if we simply calculated the discriminant. b2 -4ac=4-4(5)<0 so there are no real answers as we found.
x2 + 5x + not really sure what that extra plus is for... this is the most you can factor it... x(x + 5)
(X^2) + 4 = 0(X^2) = -4X = +/- 2i(X+2i)(X-2i)This can't be factorised easily. The above method is the factorisation for (X^2) - 4,and is also the difference of two squares (9-4) = (3+2)(3-2) etc...
It is 6+2i. But -6-2i will also serve.
1/2i
so x squared + 12 = 0 so xsquared = -12 which lands you in the realm of imaginary numbers. The square root of -12 is 2i root 3 where i is the imaginary sqrt of -1.
You don't, if you're only looking for real number results. If you are including imaginary numbers, x2+4 = (x+2i)*(x-2i).
7 + 2i
8
6+2i
1.75 + 1.75i7i/2 + 2i = 3.5i + 2i = 5.5i