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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?

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

1 Answer 1

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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: $$x=\frac{b \pm{\sqrt{b^2 - 4ac}}}{2a}$$ $$x=\frac{30 \pm{\sqrt{-4900}}}{50}$$ $$x=\frac{30 \pm{\sqrt{4900}i}}{50}$$ $$x=\frac{30 \pm{70i}}{50}$$ $$x=\frac{3 \pm{7i}}{5}$$ $$x=\frac{3+{7i}}{5},\frac{3-{7i}}{5}$$

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

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