Q41. Solve the equation by using the ... [FREE SOLUTION]

91影视

Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 9: Q41. (page 595)

Solve the equation by using the Quadratic formula. Round to the nearest tenth if necessary.
$2 f^{2} + 7 f 鈭� 15 = 0$

Short Answer

Expert verified

Thesolutions of the quadratic equations are $\frac{3}{2}$ androle="math" localid="1647852397706" $- 5$ .

Step by step solution

Step 1. Understand the concept used.

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

Step 2. Substitute the values.

It is given that $2 f^{2} + 7 f 鈭� 15 = 0$ . Using the quadratic formula $f = \frac{鈭� b 卤 \sqrt{b^{2} 鈭� 4 a c}}{2 a}$ , substitute 2 for $a, 7$ for $b$ and $- 15$ for $c$ .

Put the values in the formula and get $f = \frac{鈭� 7 卤 \sqrt{{(7)}^{2} 鈭� 4 脳 (2) 脳 (鈭� 15)}}{2 (2)}$ .

Step 3. Write the solutions.

Simplify the expression for $f$ .

$f = \frac{鈭� 7 卤 \sqrt{{(7)}^{2} 鈭� 4 脳 (2) 脳 (鈭� 15)}}{2 (2)}$

$= \frac{鈭� 7 卤 \sqrt{49 + 120}}{4} = \frac{鈭� 7 卤 \sqrt{169}}{4} = \frac{鈭� 7 卤 13}{4}$

Therefore, either

$f = \frac{鈭� 7 + 13}{4} = \frac{3}{2}$

or,

$f = \frac{鈭� 7 鈭� 13}{4} = 鈭� 5$

that is., either $f = \frac{3}{2}$ or $f = 鈭� 5$ .

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91影视

Solve the equation by using the Quadratic formula. Round to the nearest tenth if necessary.
$2 f^{2} + 7 f 鈭� 15 = 0$

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.

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91影视

Solve the equation by using the Quadratic formula. Round to the nearest tenth if necessary.2f2+7f鈭�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

Applied Mathematics

Logic and Functions

Mechanics Maths

Geometry

Theoretical and Mathematical Physics

Decision Maths

Study anywhere. Anytime. Across all devices.

Solve the equation by using the Quadratic formula. Round to the nearest tenth if necessary.
$2 f^{2} + 7 f 鈭� 15 = 0$