p+5=(1-p)^(1/2)

Solution for p+5=(1-p)^(1/2) equation:

p+5=(1-p)^(1/2)

We move all terms to the left:

p+5-((1-p)^(1/2))=0

We add all the numbers together, and all the variables

p-((-1p+1)^(+1/2))+5=0

We multiply all the terms by the denominator


p*2))-((-1p+1+1)^(+5*2))=0

We add all the numbers together, and all the variables

p*2))-((-1p+2)^10)=0

We add all the numbers together, and all the variables

-1p+p*2))-((=0

Wy multiply elements

2p^2-1p=0

a = 2; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·2·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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