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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 80 E (page 885)

In the following exercises, solve by completing the square.
$n^{2} - 2 n = - 3$

Short Answer

Expert verified

The solution is $n = 1 - i \sqrt{2}, n = 1 + i \sqrt{2}$

Step by step solution

01

Step 1. Given information

Equation: $n^{2} - 2 n = - 3$

02

Step 2. Calculation

We have,

$n^{2} - 2 n = - 3$

$n^{2} - 2 n + {(\frac{1}{2} \cdot (- 2))}^{2} = - 3 + {(\frac{1}{2} \cdot (- 2))}^{2}$

$n^{2} - 2 n + 1 = - 3 + 1$

${(n - 1)}^{2} = - 2$

$\sqrt{{(n - 1)}^{2}} = \sqrt{- 2}$

$n - 1 = \pm i \sqrt{2}$

$n - 1 + 1 = 1 - i \sqrt{2}, n - 1 + 1 = 1 + i \sqrt{2}$

$n = 1 - i \sqrt{2}, n = 1 + i \sqrt{2}$

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Most popular questions from this chapter

In the following exercises, solve by using the Quadratic Formula.

$8 x^{2} - 6 x + 2 = 0$

Identify the most appropriate method to use to solve each quadratic equation.

$a) 8 a^{2} + 3 a - 9 = 0 b) 4 b^{2} + 4 b + 1 = 0 c) 5 c^{2} = 125$

Roy kayaked up the river and then back in a total time of 6 hours. The trip was 4 miles each way and the current was difficult. If Roy kayaked at a speed of 5 mph, what was the speed of the current?

Solve quadratic equation $64 x^{2} + 144 x + 81 = 25$ using square root property

A rectangular garden will be divided into two plots by fencing it on the diagonal. The diagonal distance from one corner of the garden to the opposite corner is five yards longer than the width of the garden. The length of the garden is three times the width. Find the length of the diagonal of the garden.

See all solutions

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