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x(x+35)=125
We move all terms to the left:
x(x+35)-(125)=0
We multiply parentheses
x^2+35x-125=0
a = 1; b = 35; c = -125;
Δ = b2-4ac
Δ = 352-4·1·(-125)
Δ = 1725
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1725}=\sqrt{25*69}=\sqrt{25}*\sqrt{69}=5\sqrt{69}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-5\sqrt{69}}{2*1}=\frac{-35-5\sqrt{69}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+5\sqrt{69}}{2*1}=\frac{-35+5\sqrt{69}}{2} $
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