I am trying to solve the equation 40x^2-18x+8=0 using the most efficient method possible but I can’t seem to figure it out.

Hey nada, and welcome!

It’s because you can’t solve that specific quadratic equation!

The reason I know this is because I used the discriminant on your equation, and it came back with a negative value, which means that your equation only has complex roots.

Basically, the discriminant is the value b^2 - 4ac.

If this value is >0, then your equation has two real roots and you can solve it.

If this value =0, then your equation has one real root and you can solve it.

If this value <0, then your equation has only complex roots and you *cannot* solve it.

Since, in your case, b^2 - 4ac = (-18)^2 - 4(40)(8) = -956 < 0, we know that your equation only has complex roots and cannot be solved (in terms of real numbers, at least).

Does that help?

But what would be the answer if I did do it by using decimals? I tried and i don’t know if my answer is right

What exactly do you mean by using decimals? Do you mean using the quadratic formula?

If I apply the quadratic formula to this quadratic equation, this is what happens:

\displaystyle x = \frac{b^2 \pm \sqrt{b^2 - 4ac}}{2a} = \frac{(-18)^2 \pm \sqrt{(-18)^2 - 4(40)(8)}}{2(40)} = \frac{(-18)^2 \pm \sqrt{-956}}{80},

but here we are now stuck and can’t proceed further (unless you know about imaginary numbers, i), because we can’t have a negative number under the square-root symbol. Numbers under the square-root *always* have to be nonnegative. Hence, this quadratic equation has no solution (in real numbers).

Does that make sense?

Yes that makes more sense, thank you so much for your help! I really appreciate it.

No problem at all!

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