# How do you solve x^2-10x+25=196?

Apr 10, 2016

See explanation...

#### Explanation:

${x}^{2} - 10 x + 25 = 196$
In order to solve quadratic equation you have to make it equal to zero.
${x}^{2} - 10 x + 25 - 196 = 0$
${x}^{2} - 10 x - 171 = 0$

Then calculate the discriminant:
[DELTA]=b^2-4*a*c =(-10)^2-4*1*(-171)= =100+684= =784
*DELTA iz a sign for discriminant.

Write a quadratic formula and input all numbers in it, and solve for x1,2.

$x 1 , 2 = \frac{- b \pm \sqrt{D E L T A}}{2 a}$
$x 1 , 2 = \frac{- \left(- 10\right) \pm \sqrt{784}}{2 \cdot 1}$
$x 1 , 2 = \frac{10 \pm 28}{2}$
$x 1 = \frac{10 + 28}{2} = \frac{38}{2} = 19$
$x 2 = \frac{10 - 28}{2} = - \frac{18}{2} = - 9$

Accordingly, there are two roots since the equation is quadratic.
The roots are: $x 1 = 19$ and $x 2 = - 9$.