Q.16 Solve each equation by factoring... [FREE SOLUTION]

91影视

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 4: Q.16 (page 163)

Solve each equation by factoring or by using the quadratic formula. The quadratic formula is:
If $a x^{2} + b x + c = 0$ , with $a 鈮� 0$ , then $x = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a}$ .
$x^{2} = 3 x + 4$

Short Answer

Expert verified

The values of x are $x = 4$ and $x = - 1$ .

Step by step solution

Step 1. Understand the concept used

If $a x^{2} + b x + c = 0$ , with $a 鈮� 0$ , then $x = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a}$ . Solving using factoring can be done by splitting the middle term of equation and then making groups and equating them to zero.

Step 2. Substitute the values

It is given that $x^{2} = 3 x + 4$ which can also be written as $x^{2} - 3 x - 4 = 0$ .Using quadratic formula $x = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a}$ , substitute 1 for a, -3 for b and -4 for c.

Put the values in the formula and get $x = \frac{- (- 3) 卤 \sqrt{{(- 3)}^{2} - 4 脳 (1) 脳 (- 4)}}{2 (1)}$ .

Step 3. Simplify for x

Simplify the expression for x.

$\begin{matrix} x = \frac{鈭� (鈭� 3) 卤 \sqrt{{(鈭� 3)}^{2} 鈭� 4 脳 (1) 脳 (鈭� 4)}}{2 (1)} \\ = \frac{3 卤 \sqrt{9 + 16}}{2} \\ = \frac{3 卤 \sqrt{25}}{2} \\ = \frac{3 卤 5}{2} \end{matrix}$

Therefore, either $x = \frac{3 + 5}{2} = \frac{8}{2}$ or $x = \frac{3 - 5}{2} = \frac{- 2}{2}$ that is., either $x = 4$ or $x = - 1$ .

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!

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 each equation by factoring or by using the quadratic formula. The quadratic formula is:
If $a x^{2} + b x + c = 0$ , with $a 鈮� 0$ , then $x = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a}$ .
$x^{2} = 3 x + 4$

Short Answer

Step by step solution

Step 1. Understand the concept used

Step 2. Substitute the values

Step 3. Simplify for x

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Geometry

Statistics

Theoretical and Mathematical Physics

Discrete Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

91影视

Solve each equation by factoring or by using the quadratic formula. The quadratic formula is:If ax2+bx+c=0, with a鈮�0, then x=-b卤b2-4ac2a.x2=3x+4

Short Answer

Step by step solution

Step 1. Understand the concept used

Step 2. Substitute the values

Step 3. Simplify for x

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Geometry

Statistics

Theoretical and Mathematical Physics

Discrete Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve each equation by factoring or by using the quadratic formula. The quadratic formula is:
If $a x^{2} + b x + c = 0$ , with $a 鈮� 0$ , then $x = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a}$ .
$x^{2} = 3 x + 4$