Chapter 9: Q17. (page 597)

Solve the equation by using the Quadratic formula. Round to the nearest tenth if necessary.
$2 x^{2} + x - 15 = 0$

Short Answer

Expert verified

Thesolutions of the quadratic equations are $- 3$ and 2.5.

Step by step solution

Step 1. Understand the concept used.

If $a x^{2} + b x + c = 0$ , with $a \neq 0$ , then $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ . 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 $2 x^{2} + x - 15 = 0$ . Using quadratic formula $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ , substitute 2 for a, 1 for b and $- 15$ for c.

Put the values in the formula and get $x = \frac{- 1 \pm \sqrt{{(1)}^{2} - 4 \times (2) \times (- 15)}}{2 (2)}$ .

Step 3. Write the solutions.

Simplify the expression for x.

$x = \frac{- 1 \pm \sqrt{{(1)}^{2} - 4 \times (2) \times (- 15)}}{2 (2)} = \frac{- 1 \pm \sqrt{121}}{4} = \frac{- 1 \pm 11}{4}$

Therefore, either

$x = \frac{- 1 + 11}{4} = \frac{5}{2} = 2.5$

or,

$x = \frac{- 1 - 11}{4} = - 3$

that is., either $x = - 3$ or $x = 2.5$ .

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 equation by using the Quadratic formula. Round to the nearest tenth if necessary.
$2 x^{2} + x - 15 = 0$

Short Answer

Step by step solution

Step 1. Understand the concept used.

Step 2. Substitute the values.

Step 3. Write the solutions.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Theoretical and Mathematical Physics

Mechanics Maths

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

Solve the equation by using the Quadratic formula. Round to the nearest tenth if necessary.2x2+x−15=0

Short Answer

Step by step solution

Step 1. Understand the concept used.

Step 2. Substitute the values.

Step 3. Write the solutions.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Theoretical and Mathematical Physics

Mechanics Maths

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

Solve the equation by using the Quadratic formula. Round to the nearest tenth if necessary.
$2 x^{2} + x - 15 = 0$