Chapter 9: Q.420. (page 982)

Solve by completing the square.
$w^{2} - 20 w = 100$

Short Answer

Expert verified

The solution is $w = \pm 10 \sqrt{2} + 10$ .

Step by step solution

Step 1. Given information.

The given equation is $w^{2} - 20 w = 100$ .

Step 2. Simplify the equation.

$\begin{array}{rcl} w^{2} - 20 w & = & 100 \\ w^{2} - 2 \cdot w \cdot 10 & = & 100 \\ w^{2} - 2 \cdot w \cdot 10 + 100 & = & 100 + 100 \dots \dots (a d d 100 o n b o t h s i d e s) \\ w^{2} - 2 \cdot w \cdot 10 + 10^{2} & = & 200 \\ {(w - 10)}^{2} & = & 200 \\ w - 10 & = & \pm \sqrt{200} \\ w - 10 & = & \pm 10 \sqrt{2} \\ w & = & \pm 10 \sqrt{2} + 10 \end{array}$

Step 3. Simplified answer.

Hence, the required solution is $w = \pm 10 \sqrt{2} + 10$ .

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Solve by completing the square.
$w^{2} - 20 w = 100$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the equation.

Step 3. Simplified answer.

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Solve by completing the square.w2-20w=100

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the equation.

Step 3. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Applied Mathematics

Logic and Functions

Statistics

Discrete Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve by completing the square.
$w^{2} - 20 w = 100$