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5(x-5)(x-5)=55
We move all terms to the left:
5(x-5)(x-5)-(55)=0
We multiply parentheses ..
5(+x^2-5x-5x+25)-55=0
We multiply parentheses
5x^2-25x-25x+125-55=0
We add all the numbers together, and all the variables
5x^2-50x+70=0
a = 5; b = -50; c = +70;
Δ = b2-4ac
Δ = -502-4·5·70
Δ = 1100
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1100}=\sqrt{100*11}=\sqrt{100}*\sqrt{11}=10\sqrt{11}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{11}}{2*5}=\frac{50-10\sqrt{11}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{11}}{2*5}=\frac{50+10\sqrt{11}}{10} $
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