# How do you solve  x^2-10x+25=0 algebraically?

Apr 1, 2016

$x = 5$

#### Explanation:

Start off by writing the brackets $\left(x +\right) \left(x +\right)$, because you know this will feature in the answer, given that there's an ${x}^{2}$.

Now you want to find two numbers that add together to make $- 10$ and multiply together to make $25$. Use trial and error by writing down or thinking about the factors of $25$, and then which ones add to $- 10$. You should come to $- 5$ and $- 5$.

This gives the brackets $\left(x - 5\right) \left(x - 5\right)$ or ${\left(x - 5\right)}^{2} = 0$

Now change around the equation to make $x$ the subject.

${\left(x - 5\right)}^{2} = 0$
$x - 5 = \sqrt{0}$
$x - 5 = 0$
$x = 5$