(x2+2x)2-11x2-22x+24=0

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Solution for (x2+2x)2-11x2-22x+24=0 equation:



(x2+2x)2-11x^2-22x+24=0
We add all the numbers together, and all the variables
-11x^2+(+x^2+2x)2-22x+24=0
We multiply parentheses
-11x^2+2x^2+4x-22x+24=0
We add all the numbers together, and all the variables
-9x^2-18x+24=0
a = -9; b = -18; c = +24;
Δ = b2-4ac
Δ = -182-4·(-9)·24
Δ = 1188
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:
$\sqrt{\Delta}=\sqrt{1188}=\sqrt{36*33}=\sqrt{36}*\sqrt{33}=6\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{33}}{2*-9}=\frac{18-6\sqrt{33}}{-18} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{33}}{2*-9}=\frac{18+6\sqrt{33}}{-18} $

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