Completing the Square

Completing the square is a method used to convert a quadratic equation into a perfect square trinomial, making it easier to solve or analyze.

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, such as $$(x - a)^2 = x^2 - 2ax + a^2$$ .

To find 'c', use the formula $$c = \left(\frac{b}{2}\right)^2$$ .

The value of 'c' is 16.

The value of 'c' is 9.

Rearrange to $$x^2 - 8x = 14$$ , then add 16 to both sides to get $$(x - 4)^2 = 30$$ , leading to $$x = 4 \pm \sqrt{30}$$ .

Rearrange to $$x^2 - 4x = 21$$ , then add 4 to both sides to get $$(x - 2)^2 = 25$$ , leading to $$x = -3, 7$$ .

The factored form is $$(x - 9)^2$$ .

The first step is to move the constant term to the other side of the equation.

It means to manipulate the equation so that one side becomes a perfect square trinomial.