Solving Mathematical Equations: The Square Root of 2 More Than Twice a Number

When solving mathematical equations, it's essential to break down the problem systematically to isolate the unknown variable. This example involves a specific type of problem where the square root of a quantity is related to a given value. In this article, we'll explore how to solve such equations step-by-step, providing a clear and understandable process.

Understanding the Problem

The problem statement is: 'The square root of 2 more than twice a certain number is 6. What is the number?' Let's denote the unknown number as x.

Setting Up the Equation

The equation based on the given problem can be expressed as:

√(2 2x) 6

Solving the Equation

Square Both Sides: To eliminate the square root, square both sides of the equation:

2 2x 36

Isolate the Unknown Term: Subtract 2 from both sides to isolate the term containing x:

2x 34

Solve for x: Divide both sides by 2 to find the value of x:

x 34 / 2 17

Hence, the unknown number is 17. By following these steps, we can systematically solve and verify the equation.

Alternative Interpretations

It's important to note that different interpretations can lead to different solutions. For instance:

If it's interpreted as √(2x 2) 6, then:

(2x 2) 36

2x 34

x 34 / 2 17

Alternatively, if it is 2√x 2 6, then:

2√x 4

√x 2

x 2^2 4

In another interpretation, if it's 2√3^n 6, then:

√3^n 3

3^n 3^2 9

3^n 27

n 3

Conclusion

The key to solving such mathematical problems is to carefully interpret the equations and follow a structured approach. By breaking down the problem into simpler steps and solving it systematically, we can arrive at accurate and reliable solutions.

Related Keywords

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Further Reading

For more detailed resources on solving algebraic equations and mathematical problems, explore our comprehensive guide to algebra, or visit relevant forums and educational resources dedicated to mathematics.