(1/2)x-12=100

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Solution for (1/2)x-12=100 equation:



(1/2)x-12=100
We move all terms to the left:
(1/2)x-12-(100)=0
Domain of the equation: 2)x!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
(+1/2)x-12-100=0
We add all the numbers together, and all the variables
(+1/2)x-112=0
We multiply parentheses
x^2-112=0
a = 1; b = 0; c = -112;
Δ = b2-4ac
Δ = 02-4·1·(-112)
Δ = 448
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:
$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{7}}{2*1}=\frac{0-8\sqrt{7}}{2} =-\frac{8\sqrt{7}}{2} =-4\sqrt{7} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{7}}{2*1}=\frac{0+8\sqrt{7}}{2} =\frac{8\sqrt{7}}{2} =4\sqrt{7} $

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