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To complete the square of $x^{2}+5 x,$ add________

   To complete the square of $x^{2}+5 x,$ add________

Precalculus

Michael Sullivan 9th Edition

Chapter 10, Problem 2

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Solved by Expert Norman Atentar

07/13/2020

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To complete the square, we need to add a term $(\frac{b}{2})^{2}$, where $b$ is the coefficient of $x$. Show more…

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To complete the square of $x^{2}+5 x,$ add________

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Key Concepts

Completing the Square

Completing the square is a technique used in algebra to transform a quadratic expression into a perfect square trinomial plus or minus a constant. This method not only simplifies the process of solving quadratic equations but also helps in analyzing the graph of a quadratic function, particularly in finding its vertex form.

Perfect Square Trinomial

A perfect square trinomial is an expression that can be factored into the square of a binomial. It has the form a² + 2ab + b², where the middle term is twice the product of the square roots of the first and last terms, enabling a neat factorization which is key in techniques like completing the square.

Quadratic Expression Manipulation

Manipulating quadratic expressions involves techniques such as completing the square, factoring, and using the quadratic formula. These methods are fundamental tools in algebra that facilitate solving equations, graphing parabolas, and understanding the properties of quadratic functions.

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