The equation that results from completing the square in the following equation. x^2−20x+75=0 is (x+2)^2 = 10
What is completing the squares method for solving the quadratic equations in one variable?
The method "completing the squares", as per the name suggests, try to make the quadratic equation of the form such that the x variable is totally covered in single squared term, as the square of a linear expression in x.
GIven;
x^2−20x+75=0
Subtract 75 from each side
x^2−20x+75 - 75 = -75
Take the coefficient of x
20
Divide by 2
10
Square it
100
Add it to each side
x^2 +5x + 100 = -75 + 100
(x+2)^2 = 10
Take the square root of each side
x+2 = 10
x = 8
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