(x+4)(x+4)=65

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Solution for (x+4)(x+4)=65 equation:



(x+4)(x+4)=65
We move all terms to the left:
(x+4)(x+4)-(65)=0
We multiply parentheses ..
(+x^2+4x+4x+16)-65=0
We get rid of parentheses
x^2+4x+4x+16-65=0
We add all the numbers together, and all the variables
x^2+8x-49=0
a = 1; b = 8; c = -49;
Δ = b2-4ac
Δ = 82-4·1·(-49)
Δ = 260
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:
$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{65}}{2*1}=\frac{-8-2\sqrt{65}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{65}}{2*1}=\frac{-8+2\sqrt{65}}{2} $

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