(1/2)(x+9)-2=7

Solution for (1/2)(x+9)-2=7 equation:

(1/2)(x+9)-2=7

We move all terms to the left:

(1/2)(x+9)-2-(7)=0


Domain of the equation: 2)(x+9)!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)(x+9)-2-7=0

We add all the numbers together, and all the variables

(+1/2)(x+9)-9=0

We multiply parentheses ..

(+x^2+1/2*9)-9=0

We multiply all the terms by the denominator


(+x^2+1-9*2*9)=0

We get rid of parentheses

x^2+1-9*2*9=0

We add all the numbers together, and all the variables

x^2-161=0

a = 1; b = 0; c = -161;
Δ = b2-4ac
Δ = 02-4·1·(-161)
Δ = 644
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:

$\sqrt{\Delta}=\sqrt{644}=\sqrt{4*161}=\sqrt{4}*\sqrt{161}=2\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{161}}{2*1}=\frac{0-2\sqrt{161}}{2}
=-\frac{2\sqrt{161}}{2}
=-\sqrt{161}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{161}}{2*1}=\frac{0+2\sqrt{161}}{2}
=\frac{2\sqrt{161}}{2}
=\sqrt{161}
$