Chapter 9: Q. 110 E (page 885)

In the following exercises, solve by completing the square.
$7 x^{2} + 4 x = - 3$

Short Answer

Expert verified

The solution is $x = - \frac{2}{7} - \frac{\sqrt{17} i}{7}, x = - \frac{2}{7} + \frac{\sqrt{17} i}{7}$

Step by step solution

Step 1. Given information

Equation: $7 x^{2} + 4 x = - 3$

Step 2. Calculation

We have,

$7 x^{2} + 4 x = - 3$

$\frac{7 x^{2} + 4 x}{7} = \frac{- 3}{7}$

$x^{2} + \frac{4 x}{7} + {(\frac{1}{2} \cdot (\frac{4}{7}))}^{2} = \frac{- 3}{7} + {(\frac{1}{2} \cdot (\frac{4}{7}))}^{2}$

$x^{2} + \frac{4 x}{7} + \frac{4}{49} = \frac{- 3}{7} + \frac{4}{49}$

${(x + \frac{2}{7})}^{2} = \frac{- 17}{49}$

$\sqrt{{(x + \frac{2}{7})}^{2}} = \sqrt{\frac{- 17}{49}}$

$x + \frac{2}{7} = \pm \frac{\sqrt{17} i}{7}$

$x + \frac{2}{7} - \frac{2}{7} = - \frac{2}{7} - \frac{\sqrt{17} i}{7}, x + \frac{2}{7} - \frac{2}{7} = - \frac{2}{7} + \frac{\sqrt{17} i}{7}$

$x = - \frac{2}{7} - \frac{\sqrt{17} i}{7}, x = - \frac{2}{7} + \frac{\sqrt{17} i}{7}$

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In the following exercises, solve by completing the square.
$7 x^{2} + 4 x = - 3$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

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In the following exercises, solve by completing the square.7x2+4x=-3

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Calculus

Pure Maths

Decision Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve by completing the square.
$7 x^{2} + 4 x = - 3$