(x^2+x-1/2)= x(x+1)-1/2 [x + (1 - square root of 3)/2][x + (1 + square root of 3)/2] = 0
Check it: x^2 + x/2 + (square root of 3)x)/2 + x/2 + 1/4 + (square root of 3)/4 - (square root of 3)x/2 - (square root of 3)/4 - 3/4 = 0
x^2 + x/2 + x/2 + [(square root of 3)x]/2 - [(square root of 3)x]/2 + (square root of 3)/4 - (square root of 3)/4 + 1/4 - 3/4 = 0
x^2 + x - 2/4 = 0
x^2 + x - 1/2 = 0 How to find this roots: Using the completing the square method:
x^2 + x - 1/2 = 0 x^2 + x = 1/2 x^2 + x + 1/4 = 1/2 + 1/4 (x + 1/2)^2 = 3/4 x + 1/2 = (plus & minus)(square root of 3/4) x = -1/2 + (square root of 3)/2 x = - 1/2 - (square root of 3)/2
That doesn't factor neatly. Applying the quadratic formula, we find two imaginary solutions: i and -i where iis the square root of negative 1.
(x - i)(x + i) where i is the imaginary square root of negative one
That doesn't factor neatly. Applying the quadratic equation, we find two imaginary solutions: (-1 plus or minus the square root of -3) divided by 2.x = -0.5 + 0.8660254037844386ix = -0.5 - 0.8660254037844386iwhere i is the square root of negative one.
5 - x^2 = (the square root of 5 minus x)(the square root of 5 plus x)
(x + 3)(x + 3)
x2 + 5x + not really sure what that extra plus is for... this is the most you can factor it... x(x + 5)
That doesn't factor neatly. Applying the quadratic formula, we find two imaginary solutions: (-5 plus or minus the square root of -15) divided by 2.x = -2.5 + 1.9364916731037085ix = -2.5 - 1.9364916731037085iwhere i is the square root of negative one.
-x2 + 2x + 48 = (-x - 6)(x - 8) = -(x + 6)(x - 8)
x^2-19x+90 (x-9) (x-10)
That becomes x^2 - x + 1
That doesn't factor neatly. Applying the quadratic equation, we find two imaginary solutions: Zero plus or minus i times the square root of 3.x = 1.7320508075688772ix = -1.7320508075688772iwhere i is the square root of negative one.
(2x-5) (x-1)
That doesn't factor neatly. Applying the quadratic formula, we find two imaginary solutions: 1 plus or minus i where i is the square root of negative one.