Chapter 9: Q. 76E (page 885)

In the following exercise, solve by completing the square.
$z^{2} + 12 z = - 11$

Short Answer

Expert verified

The required solution is $z = - 1$ .

Step by step solution

Step 1. Given Information

We are given the quadratic equation

$z^{2} + 12 z = - 11$

Step 2. Calculation

$z^{2} + 12 z = - 11$

$\Rightarrow z^{2} + 12 z + {(\frac{12}{2})}^{2} = - 11 + {(\frac{12}{2})}^{2}$ take half of $12$ , square it and add it to both sides

$\Rightarrow z^{2} + 12 z + 36 = - 11 + 36$

$\Rightarrow z^{2} + 12 z + 36 = 25$ simplify

$\Rightarrow {(z + 6)}^{2} = 25$ write it as binomial squared

$\Rightarrow z + 6 = 5$ take square root on each side

$\Rightarrow z = - 1$ simplify

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In the following exercise, solve by completing the square.
$z^{2} + 12 z = - 11$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

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In the following exercise, solve by completing the square.z2+12z=-11

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Probability and Statistics

Mechanics Maths

Statistics

Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercise, solve by completing the square.
$z^{2} + 12 z = - 11$