1/2x+1/2x=x+11

Solution for 1/2x+1/2x=x+11 equation:

1/2x+1/2x=x+11

We move all terms to the left:

1/2x+1/2x-(x+11)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x+1/2x-x-11=0

We multiply all the terms by the denominator


-x*2x-11*2x+1+1=0

We add all the numbers together, and all the variables

-x*2x-11*2x+2=0

Wy multiply elements

-2x^2-22x+2=0

a = -2; b = -22; c = +2;
Δ = b2-4ac
Δ = -222-4·(-2)·2
Δ = 500
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:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-10\sqrt{5}}{2*-2}=\frac{22-10\sqrt{5}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+10\sqrt{5}}{2*-2}=\frac{22+10\sqrt{5}}{-4}
$