How do you solve non-factorable equations?

Answer 1

If your equation is in the form ax2 + bx + c, it can always be solved for x by using the quadratic formula.

x = -b plus or minus the square root of (b2 - 4ac) with the whole thing divided by 2a

Let's try an easy example: x2 + 3x - 4 = 0

That's factorable: (x + 4)(x - 1) so we already know what the answers are (-4, 1)

Now let's plug in the quadratic formula where a = 1, b = 3, c = -4

x = -3 plus or minus the square root of (3)2 -(4)1(-4) divided by 2(1)

Simplified, that's -3 plus or minus the square root of 25 divided by 2

Our two answers are (-3 + 5) divided by 2 and (-3 - 5) divided by 2

2/2 = 1 and -8/2 = -4

Non-factorable equations work just as well, except the answer won't be a whole number. It'll be some nasty decimal or an imaginary number.