(1/4)(x+2)+5=-x

Solution for (1/4)(x+2)+5=-x equation:

(1/4)(x+2)+5=-x

We move all terms to the left:

(1/4)(x+2)+5-(-x)=0


Domain of the equation: 4)(x+2)!=0

x∈R


We add all the numbers together, and all the variables

(+1/4)(x+2)-(-1x)+5=0

We get rid of parentheses

(+1/4)(x+2)+1x+5=0

We multiply parentheses ..

(+x^2+1/4*2)+1x+5=0

We multiply all the terms by the denominator


(+x^2+1+1x*4*2)+5*4*2)=0

We add all the numbers together, and all the variables

(+x^2+1+1x*4*2)=0

We get rid of parentheses

x^2+1x*4*2+1=0

Wy multiply elements

x^2+8x*2+1=0

Wy multiply elements

x^2+16x+1=0

a = 1; b = 16; c = +1;
Δ = b2-4ac
Δ = 162-4·1·1
Δ = 252
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-6\sqrt{7}}{2*1}=\frac{-16-6\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+6\sqrt{7}}{2*1}=\frac{-16+6\sqrt{7}}{2}
$