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(5x+5)(5x+5)-(5x-5)(5x-5)=(5x+5)(5x-5)
We move all terms to the left:
(5x+5)(5x+5)-(5x-5)(5x-5)-((5x+5)(5x-5))=0
We use the square of the difference formula
25x^2+(5x+5)(5x+5)-(5x-5)(5x-5)+25=0
We multiply parentheses ..
25x^2+(+25x^2+25x+25x+25)-(5x-5)(5x-5)+25=0
We get rid of parentheses
25x^2+25x^2+25x+25x-(5x-5)(5x-5)+25+25=0
We multiply parentheses ..
25x^2+25x^2-(+25x^2-25x-25x+25)+25x+25x+25+25=0
We add all the numbers together, and all the variables
50x^2-(+25x^2-25x-25x+25)+50x+50=0
We get rid of parentheses
50x^2-25x^2+25x+25x+50x-25+50=0
We add all the numbers together, and all the variables
25x^2+100x+25=0
a = 25; b = 100; c = +25;
Δ = b2-4ac
Δ = 1002-4·25·25
Δ = 7500
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7500}=\sqrt{2500*3}=\sqrt{2500}*\sqrt{3}=50\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-50\sqrt{3}}{2*25}=\frac{-100-50\sqrt{3}}{50} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+50\sqrt{3}}{2*25}=\frac{-100+50\sqrt{3}}{50} $
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