Chapter 1: Q. 30 (page 29)

In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.
$5 x^{2} = 13 x + 6$

Short Answer

Expert verified

The required solution is $x = - \frac{2}{5}, 3$ and the graph of the solution is shown below:

Step by step solution

Step 1. Given information.

We have:

$5 x^{2} = 13 x + 6$

Step 2. Solve the equation algebraically.

The equation is $5 x^{2} = 13 x + 6$ .

$5 x^{2} - 13 x - 6 = 0$

For a quadratic equation of the form $a x^{2} + b x + c = 0$ the solutions are:

$x_{1, 2} = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

For $a = 5, b = - 13, c = - 6$

$x_{1, 2} = \frac{- (- 13) \pm \sqrt{{(- 13)}^{2} - 4 \cdot 5 (- 6)}}{2 \cdot 5} x_{1, 2} = \frac{- (- 13) \pm 17}{2 \cdot 5} x = 3, - \frac{2}{5}$

Step 3. Verify the solution using a graphing utility.

The solution of the equation is $x = - \frac{2}{5}, 3$ .

Draw the graph of the equation $5 x^{2} = 13 x + 6$ using the graphing utility:

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In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.
$5 x^{2} = 13 x + 6$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solve the equation algebraically.

Step 3. Verify the solution using a graphing utility.

One App. One Place for Learning.

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In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.5x2=13x+6

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solve the equation algebraically.

Step 3. Verify the solution using a graphing utility.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Statistics

Mechanics Maths

Calculus

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.
$5 x^{2} = 13 x + 6$