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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.437. (page 983)

Solve by using the quadratic formula.
$r^{2} - r - 42 = 0$

Short Answer

Expert verified

The solution is $r = 7$ and $r = - 6$ .

Step by step solution

01

Step 1. Given information.

The given equation is $r^{2} - r - 42 = 0$ .

02

Step 2. Write the equation in standard form.

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

$\begin{array}{rcl} r^{2} - r - 42 & = & 0 \\ r^{2} + (- 1) r + (- 42) & = & 0 \end{array}$

So, here $a = 1, b = - 1, c = - 42$ .

03

Step 3. Apply the quadratic formula.

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

$\begin{array}{rcl} r & = & \frac{- (- 1) 卤 \sqrt{{(- 1)}^{2} - 4 脳 1 脳 (- 42)}}{2 脳 1} \\ = & \frac{1 卤 \sqrt{1 + 168}}{2} \\ = & \frac{1 卤 \sqrt{169}}{2} \\ = & \frac{1 卤 13}{2} \end{array}$

04

Step 4. Solve the equation for r.

$\begin{array}{rcl} r & = & \frac{1 + 13}{2} \\ = & \frac{14}{2} \\ = & 7 \end{array}$ and $\begin{array}{rcl} r & = & \frac{1 - 13}{2} \\ = & \frac{- 12}{2} \\ = & - 6 \end{array}$

05

Step 5. Simplified answer.

Hence, the required solution is $r = 7$ and $r = - 6$ .

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