2x-(x+2)(x-2)=5-(x-1)2

Solution for 2x-(x+2)(x-2)=5-(x-1)2 equation:

2x-(x+2)(x-2)=5-(x-1)2

We move all terms to the left:

2x-(x+2)(x-2)-(5-(x-1)2)=0

We use the square of the difference formula

x^2+2x-(5-(x-1)2)+4=0


We calculate terms in parentheses: -(5-(x-1)2), so:

5-(x-1)2

determiningTheFunctionDomain
-(x-1)2+5

We multiply parentheses

-2x+2+5

We add all the numbers together, and all the variables

-2x+7

Back to the equation:

-(-2x+7)


We get rid of parentheses

x^2+2x+2x-7+4=0

We add all the numbers together, and all the variables

x^2+4x-3=0

a = 1; b = 4; c = -3;
Δ = b2-4ac
Δ = 42-4·1·(-3)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{7}}{2*1}=\frac{-4-2\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{7}}{2*1}=\frac{-4+2\sqrt{7}}{2}
$