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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 88E (page 885)

In the following exercise, solve by completing the square,
$z^{2} + 2 z - 5 = 2$

Short Answer

Expert verified

The solution is $2 \sqrt{2} - 1, - 2 \sqrt{2} - 1$

Step by step solution

01

Step 1. Given information

The equation: $z^{2} + 2 z - 5 = 2$

02

Step 2. Calculation

Solving the equation,

$z^{2} + 2 z - 5 = 2$

$\Rightarrow z^{2} + 2 z = 7 \Rightarrow z^{2} + 2 z + {(\frac{1}{2} \times 2)}^{2} = 7 + {(\frac{1}{2} \times 2)}^{2}$

$\Rightarrow z^{2} + 2 z + 1 = 8 \Rightarrow z^{2} + z + z + 1 = 8$

$\Rightarrow z (z + 1) + 1 (z + 1) = 8 \Rightarrow {(z + 1)}^{2} = 8$

$\Rightarrow z + 1 = \pm \sqrt{8} \Rightarrow z = \pm 2 \sqrt{2} - 1$

The value of $z$ is $2 \sqrt{2} - 1, - 2 \sqrt{2} - 1$

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Most popular questions from this chapter

Solve :- ${(x - 5)}^{2} + 6 (x - 5) + 8 = 0$

The sun casts a shadow from a flag pole. The height of the flag pole is three times the length of its shadow. The distance between the end of the shadow and the top of the flag pole is 20 feet. Find the length of the shadow and the length of the flag pole. Round to the nearest tenth.

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

$6 x^{2} + 2 x - 20 = 0$

The distance between opposite corners of a rectangular field is four more than the width of the field. The length of the field is twice its width. Find the distance between the opposite corners. Round to the nearest tenth.

Determine the number and type of solutions to each quadratic equation.

$a) b^{2} + 7 b - 13 = 0 b) 5 a^{2} - 6 a + 10 = 0 c) 4 r^{2} - 20 r + 25 = 0$

See all solutions

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