For this equation x^(2) + x + 2

Question

which you can't factor

but then you can use the quadratic formula

but than why is the answer no real solutions when I can use the quadratic formula?

Answer 1

did you mean the equation
x^2 + x + 2 = 0 ?

When you solve an equation of the form
ax^2 + bx + c =0 you are really just asking,
"where does the graph of the corresponding function
y = ax^2 + bx + c cross the x-axis"?

In your case the graph, which is a parabola, lies totally above the x-axis, thus no x-intercepts , and thus no real solution.

If the b^2 - 4ac part of the formula is zero, there will be only one solution.
If the b^2 - 4ac part of the formula is positive, there will be 2 different real solutions.
If the b^2 - 4ac part of the formula is negative, like in your case, there will be no real solution at all.
(there will be two imaginary solutions)

Answer 2

thank you
I forgot about having a negative for b^2 - 4ac was no real solutions