Question

What is the solutions to the equation below x^2+10x+25=2
If there are more then one that’s ok

Answer 1

Answer:

$x1=-5+\sqrt{2} \\x2=-5-\sqrt{2}$

Step-by-step explanation:

First we need to simplify your equation by grouping coefficients:

$x^{2} +10x+23=0$

Now, there are two valid values for your variable, wich are determined by the following expressions:

$x=\frac{-b+\sqrt{b^{2}-4ac } }{2a} \\\\x=\frac{-b-\sqrt{b^{2}-4ac } }{2a}$

We will call those expression as (eq1) and (eq2) in their respective order

In both scenarios the following is derived from your grouped equation.

$a=1\\b=10\\c=23$

$x1=\frac{-10+\sqrt{10^{2}-4*1*23 } }{2*1}\\x2=\frac{-10-\sqrt{10^{2}-4*1*23 } }{2*1}$

$x1=\frac{-10+\sqrt{8 } }{2}\\\\x2=\frac{-10-\sqrt{8} }{2}$

We can simplify these expressions a little more by doing the following

$x1=\frac{-10+2 \sqrt{2 } }{2}\\\\x2=\frac{-10-2\sqrt{2} }{2}$

The result is

$x1=-5+\sqrt{2} \\x2=-5-\sqrt{2}$

We can not simplify these expresions anymore