Completing the Square

Completing the square is a method used to solve quadratic equations by rewriting them in the form of a perfect square trinomial, which makes it easier to solve for the variable.

The standard form of a quadratic equation is $$ax^2 + bx + c = 0$$ , where $$a$$ , $$b$$ , and $$c$$ are constants and @@a eq 0@@.

The value of 'c' can be found using the formula $$C = \frac{b}{2}^2$$ .

1. Move 5 to the left: $$x^2 + 6x - 5 = 0$$ . 2. Find 'c': $$C = \frac{6}{2}^2 = 9$$ . 3. Rewrite: $$(x + 3)^2 = 14$$ .

A perfect square trinomial is an expression that can be factored into the square of a binomial, such as $$x^2 - 18x + 81 = (x - 9)^2$$ .

You need to move the term $$-4x$$ to the other side of the equation.

The first step is to isolate the constant term on one side of the equation.

In the equation, 'b' is the coefficient of the linear term, which is 6 in this case.

The sum of the roots is equal to $$-\frac{b}{a}$$ and the product of the roots is equal to $$\frac{c}{a}$$ .

The vertex represents the maximum or minimum point of the parabola described by the quadratic function.