Chapter 9: Q.433. (page 983)

Solve by completing the square.
$2 x^{2} + 6 x = - 5$

Short Answer

Expert verified

The solution is $x = \pm \frac{1}{2} i - \frac{3}{2}$ .

Step by step solution

Step 1. Given information.

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

Step 2. Simplify the equation.

$\begin{array}{rcl} 2 x^{2} + 6 x & = & - 5 \\ \frac{2 x^{2}}{2} + \frac{6 x}{2} & = & - \frac{5}{2} \\ x^{2} + 3 x & = & - \frac{5}{2} \\ x^{2} + 2 \cdot x \cdot \frac{3}{4} & = & - \frac{5}{2} \\ x^{2} + 2 \cdot x \cdot \frac{3}{2} + {(\frac{3}{2})}^{2} & = & - \frac{5}{2} + {(\frac{3}{2})}^{2} \\ {(x + \frac{3}{2})}^{2} & = & - \frac{5}{2} + \frac{9}{4} \\ {(x + \frac{3}{2})}^{2} & = & \frac{- 10 + 9}{4} \\ {(x + \frac{3}{2})}^{2} & = & - \frac{1}{4} \end{array}$

Step 3. Solve the equation for x.

$\begin{array}{rcl} {(x + \frac{3}{2})}^{2} & = & - \frac{1}{4} \\ x + \frac{3}{2} & = & \pm \sqrt{\frac{- 1}{4}} \\ x + \frac{3}{2} & = & \pm \sqrt{\frac{1}{4}} \cdot \sqrt{- 1} \\ x + \frac{3}{2} & = & \pm \frac{1}{2} i \dots \dots (i = \sqrt{- 1}) \\ x & = & \pm \frac{1}{2} i - \frac{3}{2} \end{array}$

Step 4. Simplified answer.

Hence, the required solution is $x = \pm \frac{1}{2} i - \frac{3}{2}$ .

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Solve by completing the square.
$2 x^{2} + 6 x = - 5$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the equation.

Step 3. Solve the equation for x.

Step 4. Simplified answer.

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Solve by completing the square.2x2+6x=-5

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the equation.

Step 3. Solve the equation for x.

Step 4. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Logic and Functions

Decision Maths

Applied Mathematics

Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve by completing the square.
$2 x^{2} + 6 x = - 5$