(1/2)(x+7)=22

Solution for (1/2)(x+7)=22 equation:

(1/2)(x+7)=22

We move all terms to the left:

(1/2)(x+7)-(22)=0


Domain of the equation: 2)(x+7)!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)(x+7)-22=0

We multiply parentheses ..

(+x^2+1/2*7)-22=0

We multiply all the terms by the denominator


(+x^2+1-22*2*7)=0

We get rid of parentheses

x^2+1-22*2*7=0

We add all the numbers together, and all the variables

x^2-307=0

a = 1; b = 0; c = -307;
Δ = b2-4ac
Δ = 02-4·1·(-307)
Δ = 1228
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:

$\sqrt{\Delta}=\sqrt{1228}=\sqrt{4*307}=\sqrt{4}*\sqrt{307}=2\sqrt{307}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{307}}{2*1}=\frac{0-2\sqrt{307}}{2}
=-\frac{2\sqrt{307}}{2}
=-\sqrt{307}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{307}}{2*1}=\frac{0+2\sqrt{307}}{2}
=\frac{2\sqrt{307}}{2}
=\sqrt{307}
$