(5x)+(1/2)(4x+8)=(25)

Solution for (5x)+(1/2)(4x+8)=(25) equation:

(5x)+(1/2)(4x+8)=(25)

We move all terms to the left:

(5x)+(1/2)(4x+8)-((25))=0


Domain of the equation: 2)(4x+8)!=0

x∈R


determiningTheFunctionDomain
5x+(1/2)(4x+8)-25=0

We add all the numbers together, and all the variables

5x+(+1/2)(4x+8)-25=0

We multiply parentheses ..

(+4x^2+1/2*8)+5x-25=0

We multiply all the terms by the denominator


(+4x^2+1+5x*2*8)-25*2*8)=0

We add all the numbers together, and all the variables

(+4x^2+1+5x*2*8)=0

We get rid of parentheses

4x^2+5x*2*8+1=0

Wy multiply elements

4x^2+80x*8+1=0

Wy multiply elements

4x^2+640x+1=0

a = 4; b = 640; c = +1;
Δ = b2-4ac
Δ = 6402-4·4·1
Δ = 409584
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:

$\sqrt{\Delta}=\sqrt{409584}=\sqrt{16*25599}=\sqrt{16}*\sqrt{25599}=4\sqrt{25599}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(640)-4\sqrt{25599}}{2*4}=\frac{-640-4\sqrt{25599}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(640)+4\sqrt{25599}}{2*4}=\frac{-640+4\sqrt{25599}}{8}
$