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.
x(x + 1)
x2 + 10x + 21 = (x + 3)(x + 7)
Plus or minus the base. If the base is X and you square it, you get X2. If you take the square root of that, you get Plus or Minus X. This is because X*X equals X2 and -X*-X also equals X2.
The quadratic expression x2+6x+8 when factorised equals (x+2)(x+4)
15 x 2 = 30
x2 + x - 30 = (x + 6)(x - 5)
x(x+4) equals x2 plus 4x
x2 + 2
x2 + 2x - 15 = (x - 3)(x + 5)
if x2 + 7 = 37, then x2 = 29 and x = ±√29
X2 or 2 times x?
x = 2