1(1/5)b=1/2

Solution for 1(1/5)b=1/2 equation:

1(1/5)b=1/2

We move all terms to the left:

1(1/5)b-(1/2)=0


Domain of the equation: 5)b!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

1(+1/5)b-(+1/2)=0

We multiply parentheses

b^2-(+1/2)=0

We get rid of parentheses

b^2-1/2=0

We multiply all the terms by the denominator


b^2*2-1=0

Wy multiply elements

2b^2-1=0

a = 2; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·2·(-1)
Δ = 8
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2}}{2*2}=\frac{0-2\sqrt{2}}{4}
=-\frac{2\sqrt{2}}{4}
=-\frac{\sqrt{2}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2}}{2*2}=\frac{0+2\sqrt{2}}{4}
=\frac{2\sqrt{2}}{4}
=\frac{\sqrt{2}}{2}
$