Chapter 9: Q.447. (page 983)

Solve by using the quadratic formula.
$\frac{1}{8} p^{2} - \frac{1}{5} p = - \frac{1}{20}$

Short Answer

Expert verified

The solution is $p = \frac{4 \pm \sqrt{6}}{5}$ .

Step by step solution

Step 1. Given information.

The given equation is $\frac{1}{8} p^{2} - \frac{1}{5} p = - \frac{1}{20}$ .

Step 2. Write the equation in standard form.

The standard form of the quadratic equation is $a p^{2} + b p + c = 0$ .

The LCM of $(8, 5, 20)$ is $80$ .

So, multiply both sides of the equation by $80$ .

$\begin{array}{rcl} 80 \times \frac{1}{8} p^{2} - 80 \times \frac{1}{5} p & = & - \frac{1}{20} \times 80 \\ 10 p^{2} - 16 p & = & - 4 \\ 10 p^{2} - 16 p + 4 & = & 0 \\ 10 p^{2} + (- 16) p + 4 & = & 0 \end{array}$

Thus, here $a = 10, b = - 16, c = 4$ .

Step 3. Apply the quadratic formula.

The quadratic formula is $p = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ .

$\begin{array}{rcl} p & = & \frac{- (- 16) \pm \sqrt{{(- 16)}^{2} - 4 \times 10 \times 4}}{2 \times 10} \dots \dots (a = 10, b = - 16, c = 4) \\ = & \frac{16 \pm \sqrt{256 - 160}}{20} \\ = & \frac{16 \pm \sqrt{96}}{20} \\ = & \frac{16 \pm 4 \sqrt{6}}{4 \times 5} \\ = & \frac{4 (4 \pm \sqrt{6})}{4 \times 5} \\ = & \frac{4 \pm \sqrt{6}}{5} \end{array}$

Step 4. Simplified answer.

Hence, the required solution is $p = \frac{4 \pm \sqrt{6}}{5}$ .

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Solve by using the quadratic formula.
$\frac{1}{8} p^{2} - \frac{1}{5} p = - \frac{1}{20}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the equation in standard form.

Step 3. Apply the quadratic formula.

Step 4. Simplified answer.

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Solve by using the quadratic formula.18p2-15p=-120

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the equation in standard form.

Step 3. Apply the quadratic formula.

Step 4. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

Solve by using the quadratic formula.
$\frac{1}{8} p^{2} - \frac{1}{5} p = - \frac{1}{20}$