Problem 4 Solve the following Type I quadr... [FREE SOLUTION]

91影视

Painless Algebra

Lynette Long

$Math Studyset 91影视 Explanations$ Math

2 Edition

Chapter 9: Problem 4

Solve the following Type I quadratic equations. $$ 2 x^{2}-32=0 $$

Short Answer

Expert verified

x = 卤4

Step by step solution

Isolate the quadratic term

Add 32 to both sides of the equation to isolate the quadratic term.\[ 2x^2 - 32 + 32 = 0 + 32 \]\[ 2x^2 = 32 \]

Solve for x虏

Divide both sides of the equation by 2 to solve for $x^2$.\[ \frac{2x^2}{2} = \frac{32}{2} \]\[ x^2 = 16 \]

Apply the square root

Take the square root of both sides to solve for $x$.\[ x = \pm \sqrt{16} \]\[ x = \pm 4 \]

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isolating the quadratic term

In solving quadratic equations, the first step is often to isolate the quadratic term. This means getting the term with the variable squared by itself on one side of the equation. For example, in the exercise equation \[2x^{2} - 32 = 0\], we need to move everything else to the other side.
We do this by adding 32 to both sides:
\[2x^{2} - 32 + 32 = 0 + 32\]
Which simplifies to:
\[2x^{2} = 32\]
Now, we have successfully isolated the quadratic term.

Square Root Method

After isolating the quadratic term, the next step is to solve for the term by taking the square root. In our equation, once we have \[2x^{2} = 32\], we can further simplify it by dividing both sides by 2:
\[\frac{2x^2}{2} = \frac{32}{2}\]
Which simplifies to:
\[x^2 = 16\]
Once we have \[x^2\] isolated, we take the square root of both sides to solve for x. When taking the square root, it鈥檚 essential to remember that there are both positive and negative roots:
\[x = \pm \sqrt{16}\]
\[x = \pm 4\]
This gives us the solutions to the equation: \[x = 4\] and \[x = -4\].

Quadratic Equations

Quadratic equations are equations of the form \[ax^2 + bx + c = 0\], where \[a, b,\] and \[c\] are constants, and \[a eq 0\]. The key characteristic of these equations is the squared term \[x^2\].
The general methods for solving quadratic equations include:

Factoring
Completing the square
Quadratic formula
Square root method

In this exercise, we used the square root method because the equation \[2x^{2} - 32 = 0\] did not have an \[x\] term. Understanding which method to use is crucial. Each method has its best use cases, and knowing them will make solving any quadratic equation much easier.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Solve the following Type I quadratic equations. $$ 2 x^{2}-32=0 $$

Short Answer

Step by step solution

Isolate the quadratic term

Solve for x虏

Apply the square root

Key Concepts

Isolating the quadratic term

Square Root Method

Quadratic Equations

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Applied Mathematics

Discrete Mathematics

Mechanics Maths

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.