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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.438. (page 983)

Solve by using the quadratic formula.
$t^{2} + 13 t + 22 = 0$

Short Answer

Expert verified

The solution is $t = - 2$ and $t = - 11$ .

Step by step solution

01

Step 1. Given information.

The given equation is $t^{2} + 13 t + 22 = 0$ .

02

Step 2. Write the equation in standard form.

The standard form of the quadratic equation is $a t^{2} + b t + c = 0$ .

$t^{2} + 13 t + 22 = 0$

So, here $a = 1, b = 13, c = 22$ .

03

Step 3. Apply the quadratic formula.

The quadratic formula is $t = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a}$ .

$\begin{array}{rcl} t & = & \frac{- 13 卤 \sqrt{{(13)}^{2} - 4 脳 1 脳 22}}{2 脳 1} \\ = & \frac{- 13 卤 \sqrt{169 - 88}}{2} \\ = & \frac{- 13 卤 \sqrt{81}}{2} \\ = & \frac{- 13 卤 9}{2} \end{array}$

04

Step 4. Solve the equation for t.

$\begin{array}{rcl} t & = & \frac{- 13 + 9}{2} \\ = & \frac{- 4}{2} \\ = & - 2 \end{array}$ and $\begin{array}{rcl} t & = & \frac{- 13 - 9}{2} \\ = & \frac{- 22}{2} \\ = & - 11 \end{array}$

05

Step 5. Simplified answer.

Hence, the required solution is $t = - 2$ and $t = - 11$ .

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