F(x)=(x+8)(8-x)

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Solution for F(x)=(x+8)(8-x) equation:



(F)=(F+8)(8-F)
We move all terms to the left:
(F)-((F+8)(8-F))=0
We add all the numbers together, and all the variables
F-((F+8)(-1F+8))=0
We multiply parentheses ..
-((-1F^2+8F-8F+64))+F=0
We calculate terms in parentheses: -((-1F^2+8F-8F+64)), so:
(-1F^2+8F-8F+64)
We get rid of parentheses
-1F^2+8F-8F+64
We add all the numbers together, and all the variables
-1F^2+64
Back to the equation:
-(-1F^2+64)
We get rid of parentheses
1F^2+F-64=0
We add all the numbers together, and all the variables
F^2+F-64=0
a = 1; b = 1; c = -64;
Δ = b2-4ac
Δ = 12-4·1·(-64)
Δ = 257
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{257}}{2*1}=\frac{-1-\sqrt{257}}{2} $
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{257}}{2*1}=\frac{-1+\sqrt{257}}{2} $

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