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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q.421. (page 982)

Solve by completing the square.
$m^{2} + 10 m - 4 = - 13$

Short Answer

Expert verified

the solution is $m = - 1$ and $m = - 9$ .

Step by step solution

01

Step 1. Given information.

The given equation is $m^{2} + 10 m - 4 = - 13$ .

02

Step 2. Simplify the equation.

$\begin{array}{rcl} m^{2} + 10 m - 4 & = & - 13 \\ m^{2} + 10 m - 4 + 4 & = & - 13 + 4 鈰� 鈰� (a d d 4 o n b o t h s i d e s) \\ m^{2} + 10 m & = & - 9 \\ m^{2} + 2 路 m 路 5 & = & - 9 \\ m^{2} + 2 路 m 路 5 + 25 & = & - 9 + 25 鈰� 鈰� (a d d 25 o n b o t h s i d e s) \\ m^{2} + 2 路 m 路 5 + 5^{2} & = & 16 \\ {(m + 5)}^{2} & = & 16 \\ m + 5 & = & 卤 \sqrt{16} \\ m + 5 & = & 卤 4 \end{array}$

03

Step 3. Solve the equation for m.

$\begin{array}{rcl} m + 5 & = & 4 \\ m & = & 4 - 5 \\ m & = & - 1 \end{array}$ and $\begin{array}{rcl} m + 5 & = & - 4 \\ m & = & - 4 - 5 \\ m & = & - 9 \end{array}$

04

Step 4. Simplified answer.

Hence, the required solution is $m = - 1$ and $m = - 9$ .

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Most popular questions from this chapter

Solve :- $x^{\frac{2}{3}} - 5 x^{\frac{1}{3}} - 14 = 0$

Solve by using the Quadratic Formula: $\frac{1}{9} d^{2} - \frac{1}{2} d = - \frac{1}{3}$

In the following exercises, solve by using the Quadratic Formula. $4 n^{2} - 9 n + 5 = 0$

In the following exercises, solve by using the Quadratic Formula: $2 p^{2} + 8 p + 5 = 0$

Use the Discriminant to Predict the Number of Solutions of a Quadratic Equation.

In the following exercises, determine the number of solutions for each quadratic equation.

$(a) 9 v^{2} - 15 v + 25 = 0 (b) 100 w^{2} + 60 w + 9 = 0 (c) 5 c^{2} + 7 c - 10 = 0$

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