4=-1+x2

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Solution for 4=-1+x2 equation:



4=-1+x2
We move all terms to the left:
4-(-1+x2)=0
We add all the numbers together, and all the variables
-(+x^2-1)+4=0
We get rid of parentheses
-x^2+1+4=0
We add all the numbers together, and all the variables
-1x^2+5=0
a = -1; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-1)·5
Δ = 20
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:
$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{5}}{2*-1}=\frac{0-2\sqrt{5}}{-2} =-\frac{2\sqrt{5}}{-2} =-\frac{\sqrt{5}}{-1} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{5}}{2*-1}=\frac{0+2\sqrt{5}}{-2} =\frac{2\sqrt{5}}{-2} =\frac{\sqrt{5}}{-1} $

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