This is a free lesson from our course in Algebra II
In this lesson you'll explore the process of completing the square for solving the
equations that cannot be easily solved by
addition,
subtraction,
multiplication,
division, and
factoring. In mathematics,
completing the square is considered a basic algebraic operation, and is often applied
without remark in any computation involving quadratic polynomials. Completing the
square is the process of finding the last term of a
perfect square trinomial. E.g. Completing the square for 2x^{2}
= 1/4  1/2 x, gives x = 1/2, 1/4. To generalize let us take an example of an equation being solved in variable x:
Remember the following major steps:
• it assumes that the equation being solved is in the variable x.
• group all like terms and move all constants to other sides of the equation.
(More text below video...)
(Continued from above)
• following this, divide each term in the equation by the coefficient of the x^{2}
term, unless the coefficient is 1.
• divide the coefficient of the x term by two; square it, and add to both
sides.
• now factor the left side as a perfect square trinomial.
• take the square root of each side and determine solution for the variable.
For example, x^{2} + y^{2} + 4x  6y
= 23 simplifies to (x + 2)^{2} + (y  3)^{2} =
36.
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