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x^2+750x+250^2=0
We add all the numbers together, and all the variables
x^2+750x+62500=0
a = 1; b = 750; c = +62500;
Δ = b2-4ac
Δ = 7502-4·1·62500
Δ = 312500
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{312500}=\sqrt{62500*5}=\sqrt{62500}*\sqrt{5}=250\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(750)-250\sqrt{5}}{2*1}=\frac{-750-250\sqrt{5}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(750)+250\sqrt{5}}{2*1}=\frac{-750+250\sqrt{5}}{2} $
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