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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 10: Q 105 (page 1195)

Solve the equation using quadratic formula.
$r^{2} - 8 r - 33 = 0$

Short Answer

Expert verified

The roots are $r = - 3, r = 11$ .

Step by step solution

01

Given Information.

The given equation is $r^{2} - 8 r - 33 = 0$ .

02

Write the quadratic equation in standard form and identify a,b,c.

The quadratic equation is in standard form.

So,

$a = 1, b = - 8, c = - 33$ .

03

Substitute the values in quadratic formula.

$r = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a} r = \frac{- (- 8) 卤 \sqrt{(- 8)^{2} - 4 (1) (- 33)}}{2 (1)} r = \frac{8 卤 \sqrt{64 + 132}}{2} r = \frac{8 卤 \sqrt{196}}{2}$

Use the square root property.

$r = \frac{8 卤 14}{2}$

04

Rewrite to show two solutions.

$r_{1} = \frac{8 + 14}{2} r_{1} = \frac{22}{2} r_{1} = 11$

and

$r_{2} = \frac{8 - 14}{2} r_{2} = \frac{- 6}{2} r_{2} = - 3$

Thus, the roots are $r = - 3, r = 11$ .

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