x*2+(1/2)x+(1/4)x+1=100

Solution for x*2+(1/2)x+(1/4)x+1=100 equation:

x*2+(1/2)x+(1/4)x+1=100

We move all terms to the left:

x*2+(1/2)x+(1/4)x+1-(100)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x*2+(+1/2)x+(+1/4)x+1-100=0

We add all the numbers together, and all the variables

x*2+(+1/2)x+(+1/4)x-99=0

We multiply parentheses

x^2+x^2+x*2-99=0

Wy multiply elements

x^2+x^2+2x-99=0

We add all the numbers together, and all the variables

2x^2+2x-99=0

a = 2; b = 2; c = -99;
Δ = b2-4ac
Δ = 22-4·2·(-99)
Δ = 796
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:

$\sqrt{\Delta}=\sqrt{796}=\sqrt{4*199}=\sqrt{4}*\sqrt{199}=2\sqrt{199}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{199}}{2*2}=\frac{-2-2\sqrt{199}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{199}}{2*2}=\frac{-2+2\sqrt{199}}{4}
$