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x2-25-10x+9x^2/25=x2
We move all terms to the left:
x2-25-10x+9x^2/25-(x2)=0
We add all the numbers together, and all the variables
9x^2/25-10x-25=0
We multiply all the terms by the denominator
9x^2-10x*25-25*25=0
We add all the numbers together, and all the variables
9x^2-10x*25-625=0
Wy multiply elements
9x^2-250x-625=0
a = 9; b = -250; c = -625;
Δ = b2-4ac
Δ = -2502-4·9·(-625)
Δ = 85000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{85000}=\sqrt{2500*34}=\sqrt{2500}*\sqrt{34}=50\sqrt{34}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-250)-50\sqrt{34}}{2*9}=\frac{250-50\sqrt{34}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-250)+50\sqrt{34}}{2*9}=\frac{250+50\sqrt{34}}{18} $
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