Answer:
No real solutions.
Step-by-step explanation:
x² + 3x + 3 = 0 This does not factor with integers, so I would use the quadratic formula.
Where ax² + bx + c = 0, x = { -b±√(b²-4ac) } / 2a
Here a =1, b = 3, and c = 3
x = { -3 ± √(3² - 4*1*3) } / 2*1
x = { -3 ± √(9-12) } / 2
x = { -3 ± √-3 } / 2
x = -3/2 + (√-3)/2 OR x = -3/2 - (√-3)/2
There are no real solutions, because √-3 is not a real number.
See the "b² - 4ac" part in the Quadratic Formula? Whenever that is negative, there are no real solutions, because you get a square root of a negative. There are no square roots for negative numbers in the Real number system.
I have included a graph in the xy-plane as a picture. See how the graph never touches the x-axis? That is another way for you to know there are no real solutions.
Hope this helps.
