(x+2)(x+1)=(x+15)2+9

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Solution for (x+2)(x+1)=(x+15)2+9 equation:



(x+2)(x+1)=(x+15)2+9
We move all terms to the left:
(x+2)(x+1)-((x+15)2+9)=0
We multiply parentheses ..
(+x^2+x+2x+2)-((x+15)2+9)=0
We calculate terms in parentheses: -((x+15)2+9), so:
(x+15)2+9
We multiply parentheses
2x+30+9
We add all the numbers together, and all the variables
2x+39
Back to the equation:
-(2x+39)
We get rid of parentheses
x^2+x+2x-2x+2-39=0
We add all the numbers together, and all the variables
x^2+x-37=0
a = 1; b = 1; c = -37;
Δ = b2-4ac
Δ = 12-4·1·(-37)
Δ = 149
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{149}}{2*1}=\frac{-1-\sqrt{149}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{149}}{2*1}=\frac{-1+\sqrt{149}}{2} $

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