To complete a square, follow these steps: start with a quadratic expression, arrange it as a square of a binomial, group the terms and factor the perfect square trinomial, then simplify and rewrite the expression.
To complete a square, follow these steps:
Start with a quadratic expression in the form of ax^2 + bx + c.
Arrange the quadratic expression as a square of a binomial by adding and subtracting a constant term, which is determined by half of the coefficient of the linear term squared.
For example, if the coefficient of the linear term is 2b, you would add and subtract (2b/2)^2 = b^2.
Group the quadratic terms together and factor the perfect square trinomial.
Write the expression as the sum of the perfect square trinomial and the remaining constant term.
Simplify and rewrite the expression.
The completed square can now be used to solve equations or find the vertex of a parabola.