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To complete the square of $x^{2}-5 x,$ you add the number _______.

   To complete the square of $x^{2}-5 x,$ you add the number _______.

Precalculus

Michael Sullivan 9th Edition

Chapter 3, Problem 3

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Solved by Expert Peter Winans

07/07/2020

Step 1

In the expression $x^{2}-5x$, the coefficient of $x^{2}$ is 1 (a = 1) and the coefficient of $x$ is -5 (b = -5). Show more…

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To complete the square of $x^{2}-5 x,$ you add the number _______.

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Key Concepts

Halving the Linear Coefficient and Squaring

This concept involves taking half of the coefficient of the x-term in a quadratic expression and then squaring it. This squared number is the crucial value added during the process of completing the square, ensuring that the quadratic becomes a perfect square trinomial.

Completing the Square

This is a method used to rewrite a quadratic expression in the form of a perfect square plus or minus a constant. It involves manipulating the expression so that one part becomes a binomial squared, which can then be used to solve equations or analyze the graph of a quadratic function.

Perfect Square Trinomial

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial. For an expression of the form x² + bx, adding (b/2)² creates a perfect square trinomial, allowing the expression to be written as (x + b/2)².

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