(1/2)(x+4)=8

Solution for (1/2)(x+4)=8 equation:

(1/2)(x+4)=8

We move all terms to the left:

(1/2)(x+4)-(8)=0


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

x∈R


We add all the numbers together, and all the variables

(+1/2)(x+4)-8=0

We multiply parentheses ..

(+x^2+1/2*4)-8=0

We multiply all the terms by the denominator


(+x^2+1-8*2*4)=0

We get rid of parentheses

x^2+1-8*2*4=0

We add all the numbers together, and all the variables

x^2-63=0

a = 1; b = 0; c = -63;
Δ = b2-4ac
Δ = 02-4·1·(-63)
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{-(0)-6\sqrt{7}}{2*1}=\frac{0-6\sqrt{7}}{2}
=-\frac{6\sqrt{7}}{2}
=-3\sqrt{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{7}}{2*1}=\frac{0+6\sqrt{7}}{2}
=\frac{6\sqrt{7}}{2}
=3\sqrt{7}
$