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Exercises Roots and quadratic equations

Example 10.14 from Elementary Algebra, 10.2 Solve Quadratic Equations by Completing the Square

Solve Quadratic Equations by Completing the Square: example 10.14

Complete the square to make a perfect square trinomial. Then, write the result as a binomial square.

$x^{2} + 14 x$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution

The coefficient of x is 14.

$\begin{matrix} Find {(\frac{1}{2} b)}^{2} . \\ {(\frac{1}{2} \cdot 14)}^{2} \\ {(7)}^{2} \\ 49 \end{matrix}$

Add 49 to the binomial to complete the square. $x^{2} + 14 x + 49$

Rewrite as a binomial square. ${(x + 7)}^{2}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Complete the square to make a perfect square trinomial. Write the result as a binomial square.

$y^{2} + 12 y$

How did it go?

PreviousSolve Quadratic Equations Using the Square Root Property: example 10.13 Next Solve Quadratic Equations by Completing the Square: example 10.15

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 10.2, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.