х^2+10х+25=0

To find the solutions for the quadratic equation \(x^2 + 10x + 25 = 0\), we can use the quadratic formula:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

In the given equation, \(a = 1\), \(b = 10\), and \(c = 25\).

Plugging these values into the quadratic formula gives:

\[ x = \frac{-10 \pm \sqrt{10^2 - 4*1*25}}{2*1} \]

\[ x = \frac{-10 \pm \sqrt{100 - 100}}{2} \]

\[ x = \frac{-10 \pm \sqrt{0}}{2} \]

Since the square root of 0 is 0, the solutions are:

\[ x = \frac{-10}{2} \]

Therefore, the only solution to the equation \(x^2 + 10x + 25 = 0\) is \(x = -5\).