(1/2)(x+8)=7

Solution for (1/2)(x+8)=7 equation:

(1/2)(x+8)=7

We move all terms to the left:

(1/2)(x+8)-(7)=0


Domain of the equation: 2)(x+8)!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)(x+8)-7=0

We multiply parentheses ..

(+x^2+1/2*8)-7=0

We multiply all the terms by the denominator


(+x^2+1-7*2*8)=0

We get rid of parentheses

x^2+1-7*2*8=0

We add all the numbers together, and all the variables

x^2-111=0

a = 1; b = 0; c = -111;
Δ = b2-4ac
Δ = 02-4·1·(-111)
Δ = 444
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:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{111}}{2*1}=\frac{0-2\sqrt{111}}{2}
=-\frac{2\sqrt{111}}{2}
=-\sqrt{111}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{111}}{2*1}=\frac{0+2\sqrt{111}}{2}
=\frac{2\sqrt{111}}{2}
=\sqrt{111}
$