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10(x-2)+19=(5x+1)(5x-1)
We move all terms to the left:
10(x-2)+19-((5x+1)(5x-1))=0
We use the square of the difference formula
25x^2+10(x-2)+1+19=0
We multiply parentheses
25x^2+10x-20+1+19=0
We add all the numbers together, and all the variables
25x^2+10x=0
a = 25; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·25·0
Δ = 100
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{100}=10$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*25}=\frac{-20}{50} =-2/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*25}=\frac{0}{50} =0 $
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