\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 Context

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.

$\Rightarrow 25k^2 + 9k^2 = 1156$

Key Insights

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

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Final Thoughts

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.