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160=(x+8)(x+6)
We move all terms to the left:
160-((x+8)(x+6))=0
We multiply parentheses ..
-((+x^2+6x+8x+48))+160=0
We calculate terms in parentheses: -((+x^2+6x+8x+48)), so:We get rid of parentheses
(+x^2+6x+8x+48)
We get rid of parentheses
x^2+6x+8x+48
We add all the numbers together, and all the variables
x^2+14x+48
Back to the equation:
-(x^2+14x+48)
-x^2-14x-48+160=0
We add all the numbers together, and all the variables
-1x^2-14x+112=0
a = -1; b = -14; c = +112;
Δ = b2-4ac
Δ = -142-4·(-1)·112
Δ = 644
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{644}=\sqrt{4*161}=\sqrt{4}*\sqrt{161}=2\sqrt{161}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{161}}{2*-1}=\frac{14-2\sqrt{161}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{161}}{2*-1}=\frac{14+2\sqrt{161}}{-2} $
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