(1/2)(4x-16)+32=x+16

Solution for (1/2)(4x-16)+32=x+16 equation:

(1/2)(4x-16)+32=x+16

We move all terms to the left:

(1/2)(4x-16)+32-(x+16)=0


Domain of the equation: 2)(4x-16)!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)(4x-16)-(x+16)+32=0

We get rid of parentheses

(+1/2)(4x-16)-x-16+32=0

We multiply parentheses ..

(+4x^2+1/2*-16)-x-16+32=0

We multiply all the terms by the denominator


(+4x^2+1-x*2*-16)-16*2*-16)+32*2*-16)=0

We add all the numbers together, and all the variables

(+4x^2+1-x*2*-16)=0

We get rid of parentheses

4x^2-x*2*+1-16=0

We add all the numbers together, and all the variables

4x^2-x*2*-15=0

Wy multiply elements

4x^2-2x^2-15=0

We add all the numbers together, and all the variables

2x^2-15=0

a = 2; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·2·(-15)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*2}=\frac{0-2\sqrt{30}}{4}
=-\frac{2\sqrt{30}}{4}
=-\frac{\sqrt{30}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*2}=\frac{0+2\sqrt{30}}{4}
=\frac{2\sqrt{30}}{4}
=\frac{\sqrt{30}}{2}
$