Math Problem Statement

What number should be added to complete the square of the following expression? x^2 - x.

Solution

To complete the square for the expression x2xx^2 - x, we follow this method:

Step 1: Coefficient of xx

The coefficient of the linear term xx is 1-1.

Step 2: Take half of the coefficient of xx

Half of 1-1 is 12\frac{-1}{2}.

Step 3: Square the result

Squaring 12\frac{-1}{2} gives: (12)2=14\left(\frac{-1}{2}\right)^2 = \frac{1}{4}

Thus, the number that should be added to complete the square is 14\frac{1}{4}.

Would you like further details or have any questions?

Here are some related questions:

  1. What is completing the square used for in solving quadratic equations?
  2. Can completing the square be applied to any quadratic expression?
  3. How do you factor a quadratic after completing the square?
  4. What happens if the coefficient of x2x^2 is not 1?
  5. How can completing the square help in deriving the quadratic formula?

Tip: Completing the square is particularly useful when solving quadratic equations that do not factor easily.

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Math Problem Analysis

Mathematical Concepts

Completing the Square
Quadratic Expressions
Algebra

Formulas

(b/2)^2 for completing the square

Theorems

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Suitable Grade Level

Grades 8-10