Completing the square is method of solving a quadratic equation that involves finding a value to add to both the left and right side of the equation. This value has the extra benefit of making one side of the equation a perfect trinomial which makes the function easier to identify and/or graph.
Let's begin by factoring 2525 from the left side of the equation.
25(x^2-(20)/25x) = 1125(x2−2025x)=11
Take the coefficient of the xx term and divide it by 22 and square it
((-20/25)/(2))^2=(-20/25*1/2)^2=(-10/25)^2=100/625(−20252)2=(−2025⋅12)2=(−1025)2=100625
100/625100625 This the number you add to the left side
25(100/625)25(100625) Is added to the right side because we initially factored out 25 from the left side.
We added these values but the equation remains balanced because they are added to both sides of the equation.
25(x^2-(20)/25x+100/625) = 11 + 25(100/625)25(x2−2025x+100625)=11+25(100625)
25(x^2-(20)/25x+100/625) = 11 + 100/2525(x2−2025x+100625)=11+10025
25(x^2-(20)/25x+100/625) = 11 + 425(x2−2025x+100625)=11+4
25(x^2-(20)/25x+100/625) = 1525(x2−2025x+100625)=15
(x^2-(20)/25x+100/625) = 15/25(x2−2025x+100625)=1525
(x-(10)/25)^2 = 15/25(x−1025)2=1525
sqrt((x-(10)/25)^2) = sqrt(15/25)√(x−1025)2=√1525
(x-(10)/25) = sqrt(15/25)(x−1025)=√1525
x = sqrt(15/25)+(10)/25x=√1525+1025
x = sqrt(15)/5+(10)/25x=√155+1025
x = sqrt(15)/5+(2)/5x=√155+25
x = (sqrt(15)+2)/5x=√15+25
