Problem Statement
To solve the equation 22x + 332.2x + 1 = 0, we first need to simplify and rearrange it into a standard quadratic form.
Step 1: Combine Like Terms
- We have two terms involving x: 22x and 332.2x.
- Combine these terms:
- 22x + 332.2x = (22 + 332.2)x = 354.2x.
Step 2: Rewrite the Equation
- The equation now reads:
- 354.2x + 1 = 0.
Step 3: Isolate x
- Rearranging gives:
- 354.2x = -1.
Step 4: Solve for x
- Divide both sides by 354.2:
- x = -1 / 354.2.
Step 5: Calculate the Value
- Performing the calculation:
- x ≈ -0.00283.
Final Answer
- The value of x is approximately -0.00283.
Conclusion
- This solution provides the value for x in the given equation.
- Always ensure to check your work by substituting x back into the original equation to verify that it equals zero.
This methodical approach can be helpful in solving similar problems in the UPSC category, where precision and clarity are paramount.