Chapter 7: Q44. (page 462)

Solve the given equation.
$2 (4 w + w^{2}) - 6 = 2 w (w - 4) + 10$

Short Answer

Expert verified

$w = 1$ is the solution of the given equation.

Step by step solution

Step 1. Define an equation.

In mathematics, an equation is a statement that asserts the equality of two expressions, which are connected by the equal sign $" = "$ .

Step 2. Define the power of a product rule.

Power of a product rule states that if the two exponents of the same base are multiplied then the exponents are added and base remains the same.

$a^{m} . a^{n} = a^{m + n}$

Where, $a$ is any non-zero real number.

Step 3. Solve the equation, 2(4w+w2)−6=2w(w−4)+10.

Use the power of a product rule to solve the equation.

$\begin{matrix} 2 (4 w + w^{2}) - 6 = 2 w (w - 4) + 10 \\ 2 (4 w) + 2 (w^{2}) - 6 = 2 w (w) - 2 w (4) + 10 \\ {8w+2w}^{2} - 6 = 2 w^{2} - 8 w + 10 \\ {8w+2w}^{2} - 2 w^{2} + 8 w = 10 + 6 \\ 16 w = 16 \\ w = \frac{16}{16} \\ w = 1 \end{matrix}$

Therefore, $w = 1$ is the solution of the given equation.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Solve the given equation.
$2 (4 w + w^{2}) - 6 = 2 w (w - 4) + 10$

Short Answer

Step by step solution

Step 1. Define an equation.

Step 2. Define the power of a product rule.

Step 3. Solve the equation, 2(4w+w2)−6=2w(w−4)+10.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Pure Maths

Logic and Functions

Calculus

Mechanics Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

Solve the given equation.2(4w+w2)−6=2w(w−4)+10

Short Answer

Step by step solution

Step 1. Define an equation.

Step 2. Define the power of a product rule.

Step 3. Solve the equation, 2(4w+w2)−6=2w(w−4)+10.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Pure Maths

Logic and Functions

Calculus

Mechanics Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

Solve the given equation.
$2 (4 w + w^{2}) - 6 = 2 w (w - 4) + 10$