solve by completing the square:
2/2-7 -1/x = 6

To solve the equation \(\frac{2}{2-7} - \frac{1}{x} = 6\) by completing the square, let's go step by step:

### Step 1: Simplify the equation
First, simplify \(\frac{2}{2-7}\):
\[
\frac{2}{2 - 7} = \frac{2}{-5} = -\frac{2}{5}
\]
So, the equation becomes:
\[
-\frac{2}{5} - \frac{1}{x} = 6
\]

### Step 2: Move constants to the other side
Add \(\frac{2}{5}\) to both sides of the equation to isolate the term involving \(x\):
\[
-\frac{1}{x} = 6 + \frac{2}{5}
\]
To add these two numbers, we need to convert 6 into a fraction:
\[
6 = \frac{30}{5}
\]
Now, add the fractions:
\[
-\frac{1}{x} = \frac{30}{5} + \frac{2}{5} = \frac{32}{5}
\]

### Step 3: Solve for \(x\)
Now, multiply both sides of the equation by -1 to get:
\[
\frac{1}{x} = -\frac{32}{5}
\]
Finally, take the reciprocal of both sides to solve for \(x\):
\[
x = -\frac{5}{32}
\]

### Final Answer:
\[
x = -\frac{5}{32}
\]

Do you need further clarification or details?

Here are 5 related questions to expand your understanding:
1. How do you solve other rational equations involving fractions?
2. What happens if the equation contains more complex fractions?
3. Can completing the square method be used for quadratic equations only?
4. How do you graph the solution of a rational equation?
5. How can you solve rational equations with variables in both the numerator and denominator?

**Tip:** Always simplify the equation as much as possible before applying any complex methods like completing the square!

solve by completing the square: 2/2-7 - 1/x = 6

Discover how to solve the rational equation 2/(2-7) - 1/x = 6 step-by-step using fraction addition and reciprocal properties. This problem involves simplifying fractions and solving for x. Ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation