X+5=(1/2)(x+2)

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

X+5=(1/2)(X+2)

We move all terms to the left:

X+5-((1/2)(X+2))=0


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

X∈R


We add all the numbers together, and all the variables

X-((+1/2)(X+2))+5=0

We multiply parentheses ..

-((+X^2+1/2*2))+X+5=0

We multiply all the terms by the denominator


-((+X^2+1+X*2*2))+5*2*2))=0


We calculate terms in parentheses: -((+X^2+1+X*2*2)), so:

(+X^2+1+X*2*2)

We get rid of parentheses

X^2+X*2*2+1

Wy multiply elements

X^2+4X*2+1

Wy multiply elements

X^2+8X+1

Back to the equation:

-(X^2+8X+1)


We add all the numbers together, and all the variables

-(X^2+8X+1)=0

We get rid of parentheses

-X^2-8X-1=0

We add all the numbers together, and all the variables

-1X^2-8X-1=0

a = -1; b = -8; c = -1;
Δ = b2-4ac
Δ = -82-4·(-1)·(-1)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{15}}{2*-1}=\frac{8-2\sqrt{15}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{15}}{2*-1}=\frac{8+2\sqrt{15}}{-2}
$