Q.430. Solve by completing the square.2... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

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.

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

Step 3. Continue the above calculation.

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

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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91影视

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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91影视

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

Theoretical and Mathematical Physics

Calculus

Logic and Functions

Geometry

Probability and Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

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