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(x+1/2x)+1=100
We move all terms to the left:
(x+1/2x)+1-(100)=0
Domain of the equation: 2x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
(+x+1/2x)+1-100=0
We add all the numbers together, and all the variables
(+x+1/2x)-99=0
We get rid of parentheses
x+1/2x-99=0
We multiply all the terms by the denominator
x*2x-99*2x+1=0
Wy multiply elements
2x^2-198x+1=0
a = 2; b = -198; c = +1;
Δ = b2-4ac
Δ = -1982-4·2·1
Δ = 39196
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{39196}=\sqrt{4*9799}=\sqrt{4}*\sqrt{9799}=2\sqrt{9799}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-198)-2\sqrt{9799}}{2*2}=\frac{198-2\sqrt{9799}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-198)+2\sqrt{9799}}{2*2}=\frac{198+2\sqrt{9799}}{4} $
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