I'm trying to find solution(s) to the following equation:

$x^2 - 5x + 3 = 0$

It seems like it can't be factored normally so I tried solving by completing the square:



$(x-2.5)^2 = -0.5$

That's where I get stuck since you can't get the real number square root of a negative number.

Is there another method I could use to solve this quadratic equation? Did I make a mistake?

  • 2
    $\begingroup$ I think you made a mistake going from $x^2-5x = -3$ to $x^2 - 5x + 6.25 = -0.5$. What did you add to both sides? $\endgroup$ – Ben Blum-Smith Nov 24 '15 at 4:28
  • $\begingroup$ Ah, you're right. I added 6.5 to the left side and only 2.5 to the right side. $\endgroup$ – spencer.sm Nov 24 '15 at 4:32
  • $\begingroup$ Not all quadratics are solvable in the real numbers, by the way. Example: $x^2 - 5x + 7 = 0$ will get you $(x - 2.5)^2 = -0.75$ which has no real number solution. $\endgroup$ – fleablood Nov 24 '15 at 4:44




Also, since you're asking for another method, try the quadratic formula. $x = \frac{-b\pm \sqrt{b^{2} - 4 ac}}{2a}$ where $a, b, c$ are the coefficients of $ax^2+bx+c=0$


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