(x-2)(x-2)=14

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Solution for (x-2)(x-2)=14 equation:



(x-2)(x-2)=14
We move all terms to the left:
(x-2)(x-2)-(14)=0
We multiply parentheses ..
(+x^2-2x-2x+4)-14=0
We get rid of parentheses
x^2-2x-2x+4-14=0
We add all the numbers together, and all the variables
x^2-4x-10=0
a = 1; b = -4; c = -10;
Δ = b2-4ac
Δ = -42-4·1·(-10)
Δ = 56
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:
$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{14}}{2*1}=\frac{4-2\sqrt{14}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{14}}{2*1}=\frac{4+2\sqrt{14}}{2} $

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