x(x+2)2=49x

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Solution for x(x+2)2=49x equation:



x(x+2)2=49x
We move all terms to the left:
x(x+2)2-(49x)=0
We add all the numbers together, and all the variables
-49x+x(x+2)2=0
We multiply parentheses
2x^2-49x+4x=0
We add all the numbers together, and all the variables
2x^2-45x=0
a = 2; b = -45; c = 0;
Δ = b2-4ac
Δ = -452-4·2·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-45}{2*2}=\frac{0}{4} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+45}{2*2}=\frac{90}{4} =22+1/2 $

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