 The equation is 0 = $$25x^2$$ - 30x + 58.

A = 25 , B = 30, C = 58

Using the quadratic formula (as shown in the picture) I get $$\dfrac{{900\pm\sqrt{(-4900)}}}{ {50}}$$. When I put it in the calculator (either the + or -, not both at the same time) I get "Non-Real Error". Is the answer not real?

• It's not real; it's imaginary. Oct 10, 2021 at 1:13
• @JamesA It is not imaginary either. It is complex with a non-zero imaginary component. Oct 10, 2021 at 1:45
• @Deepak Whoops, yeh you're right. Oct 10, 2021 at 1:46

The solution for this equation is imaginary solutions or complex solution. To check it, use the formula $$b^2-4ac$$.

If $$b^2-4ac$$ is more than 0, then it has different real solution. For instance, x = 2 and x = 3.

If $$b^2-4ac$$ is equal to 0, then it has same real solution. For instance, x = 3 and x = 3.

If $$b^2-4ac$$ is less than 0, then it has complex solution. For instance, $$x = 2 + 3i$$ and $$x = 2 - 3i$$ where i is referring to imaginary number or $$\sqrt{-1}$$

In this case, a = 25, b = -30 and c = 58. By using the formula: $$b^2-4ac=(-30)^2-4(25)(58)$$ $$b^2-4ac=900-5800$$ $$b^2-4ac=-4900 < 0$$

Hence it has complex solution or no real solution (no solution).

So, to solve it, just use Quadratic Formula: $$x=\frac{b \pm{\sqrt{b^2 - 4ac}}}{2a}$$ $$x=\frac{30 \pm{\sqrt{-4900}}}{50}$$ $$x=\frac{30 \pm{\sqrt{4900}i}}{50}$$ $$x=\frac{30 \pm{70i}}{50}$$ $$x=\frac{3 \pm{7i}}{5}$$ $$x=\frac{3+{7i}}{5},\frac{3-{7i}}{5}$$

• I didn't realize you could divide the 70i by ten as well. Thank you Oct 10, 2021 at 2:03
• You are welcome.
– user958619
Oct 10, 2021 at 2:06