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(3x+3)2+(4x)2=174
We move all terms to the left:
(3x+3)2+(4x)2-(174)=0
We add all the numbers together, and all the variables
4x^2+(3x+3)2-174=0
We multiply parentheses
4x^2+6x+6-174=0
We add all the numbers together, and all the variables
4x^2+6x-168=0
a = 4; b = 6; c = -168;
Δ = b2-4ac
Δ = 62-4·4·(-168)
Δ = 2724
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2724}=\sqrt{4*681}=\sqrt{4}*\sqrt{681}=2\sqrt{681}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{681}}{2*4}=\frac{-6-2\sqrt{681}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{681}}{2*4}=\frac{-6+2\sqrt{681}}{8} $
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