Chapter 9.4, Problem 11E

To determine

To complete the square for expression.Then factor the trinomial.

  $x^2-10x$

Answer to Problem 11E

  $x^2-10x+25$

  $x^2-10x+25={(x-5)}^2$

Explanation of Solution

Given information:

Expression

  $x^2-10x$

Calculation:

Expression

  $x^2-10x$

Using the complete square algorithm

Step 1: Find $\frac{1}{2}$ of $-10$

  $=\frac{1}{2}\times -10$

On solving

  $=-5$

Step 2: Square the result in step 1

  ${(-5)}^2=25$

Step 3: Add the result of step 2 to $x^2-10x$

Thus $c=25$

Notice that $x^2-10x+25$

  $x^2-2\times x\times 5+25$

On solving

  $x^2-2\times x\times 5+5^2$

Using $a^2-2ab+b^2={(a-b)}^2$

Then

  $x^2-10x+25={(x-5)}^2$