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5x^2-5x-25=0*
We move all terms to the left:
5x^2-5x-25-(0*)=0
We add all the numbers together, and all the variables
5x^2-5x-25-0=0
We add all the numbers together, and all the variables
5x^2-5x-25=0
a = 5; b = -5; c = -25;
Δ = b2-4ac
Δ = -52-4·5·(-25)
Δ = 525
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{525}=\sqrt{25*21}=\sqrt{25}*\sqrt{21}=5\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{21}}{2*5}=\frac{5-5\sqrt{21}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{21}}{2*5}=\frac{5+5\sqrt{21}}{10} $
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