x(x+2)+72=180

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Solution for x(x+2)+72=180 equation:



x(x+2)+72=180
We move all terms to the left:
x(x+2)+72-(180)=0
We add all the numbers together, and all the variables
x(x+2)-108=0
We multiply parentheses
x^2+2x-108=0
a = 1; b = 2; c = -108;
Δ = b2-4ac
Δ = 22-4·1·(-108)
Δ = 436
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:
$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{109}}{2*1}=\frac{-2-2\sqrt{109}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{109}}{2*1}=\frac{-2+2\sqrt{109}}{2} $

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