Chapter 9: Q.430. (page 983)

Solve by completing the square.
$2 x^{2} + 2 x = 4$

Short Answer

Expert verified

The Solution is $x = - 2$ and $x = 1$ .

Step by step solution

Step 1. Given information.

The given equation is $2 x^{2} + 2 x = 4$ .

Step 2. Simplify the given equation.

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

Step 3. Continue the above calculation.

$\begin{array}{rcl} {(x + \frac{1}{2})}^{2} & = & \frac{9}{4} \\ x + \frac{1}{2} & = & \pm \sqrt{\frac{9}{4}} \\ x + \frac{1}{2} & = & \pm \frac{3}{2} \end{array}$

Step 4. Solve the equation for x.

$\begin{array}{rcl} x + \frac{1}{2} & = & \frac{3}{2} \\ x & = & \frac{3}{2} - \frac{1}{2} \\ x & = & \frac{3 - 1}{2} \\ x & = & \frac{2}{2} \\ x & = & 1 \end{array}$ and $\begin{array}{rcl} x + \frac{1}{2} & = & - \frac{3}{2} \\ x & = & - \frac{3}{2} - \frac{1}{2} \\ x & = & \frac{- 3 - 1}{2} \\ x & = & \frac{- 4}{2} \\ x & = & - 2 \end{array}$

Step 5. Simplified answer.

Hence, the required solution is $x = 1$ and $x = - 2$ .

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Solve by completing the square.
$2 x^{2} + 2 x = 4$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the given equation.

Step 3. Continue the above calculation.

Step 4. Solve the equation for x.

Step 5. Simplified answer.

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Solve by completing the square.2x2+2x=4

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the given equation.

Step 3. Continue the above calculation.

Step 4. Solve the equation for x.

Step 5. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Calculus

Geometry

Pure Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Solve by completing the square.
$2 x^{2} + 2 x = 4$