(1/2)(4x-10)+5=x-11

Solution for (1/2)(4x-10)+5=x-11 equation:

(1/2)(4x-10)+5=x-11

We move all terms to the left:

(1/2)(4x-10)+5-(x-11)=0


Domain of the equation: 2)(4x-10)!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)(4x-10)-(x-11)+5=0

We get rid of parentheses

(+1/2)(4x-10)-x+11+5=0

We multiply parentheses ..

(+4x^2+1/2*-10)-x+11+5=0

We multiply all the terms by the denominator


(+4x^2+1-x*2*-10)+11*2*-10)+5*2*-10)=0

We add all the numbers together, and all the variables

(+4x^2+1-x*2*-10)=0

We get rid of parentheses

4x^2-x*2*+1-10=0

We add all the numbers together, and all the variables

4x^2-x*2*-9=0

Wy multiply elements

4x^2-2x^2-9=0

We add all the numbers together, and all the variables

2x^2-9=0

a = 2; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·2·(-9)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{2}}{2*2}=\frac{0-6\sqrt{2}}{4}
=-\frac{6\sqrt{2}}{4}
=-\frac{3\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{2}}{2*2}=\frac{0+6\sqrt{2}}{4}
=\frac{6\sqrt{2}}{4}
=\frac{3\sqrt{2}}{2}
$