\Rightarrow 25k^2 + 9k^2 = 1156
How to Solve 25k² + 9k² = 1156: A Step-by-Step Guide
If you’ve stumbled upon the equation 25k² + 9k² = 1156 and wonder how to solve it, you're not alone—equations like this appear frequently in algebra and math coursework. Whether you’re a high school student, a homeschooling parent, or someone brushing up on foundational math, this guide breaks down the process step-by-step to make solving for k fast and easy.
Understanding the Equation
At first glance, the equation looks simple: 25k² + 9k² = 1156
But combining like terms is the key to simplifying and solving it.
Step 1: Combine Like Terms
Both terms on the left-hand side involve k², so you can add their coefficients: 25k² + 9k² = (25 + 9)k² = 34k²
So, the equation becomes: 34k² = 1156
Step 2: Isolate k²
To isolate k², divide both sides by 34: k² = 1156 ÷ 34
Now compute the division: 1156 ÷ 34 = 34
So: k² = 34
Step 3: Solve for k
Now take the square root of both sides: k = ±√34
Since √34 is an irrational number (approximately 5.83), the solutions are: k = √34 and k = –√34
Why This Formula Matters
This type of quadratic simplification is fundamental in algebra. Understanding how to combine like terms, isolate variables, and take square roots equips you to solve more complex equations in physics, engineering, and advanced math.
Summary: The Key Steps
- Combine like terms: 25k² + 9k² = 34k²
- Divide both sides by coefficient: k² = 1156 ÷ 34 = 34
- Take square root: k = ±√34
Final Answer
k = √34 ≈ 5.83 (and negative counterpart)
Bonus Tips for Beginners
- Always simplify expressions before solving.
- Double-check your division to avoid rounding errors.
- Remember, square roots yield both positive and negative solutions.
If you’re learning algebra or preparing for exams, mastering equations like 25k² + 9k² = 1156 sets a solid foundation for future success. Practice simple combining and solving steps daily, and soon algebra will feel much more manageable!
For more math help, explore free online calculators, video tutorials, and step-by-step guides to strengthen your skills every day.
