\Rightarrow 25k^2 + 9k^2 = 1156 - Anadea
How to Solve 25k² + 9k² = 1156: A Step-by-Step Guide
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.
Image Gallery
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
🔗 Related Articles You Might Like:
📰 A research grant requires that a number of distinct positive integers each less than or equal to 50 be selected such that each is congruent to 3 modulo 7. What is the total number of such integers? 📰 So $ k = 0, 1, 2, 3, 4, 5, 6 $, yielding 7 values. 📰 In a carbon capture model, a nanotech matrix cycles through states labeled by integers from 1 to 100. The system activates only when the sum of three consecutive integers in this range is divisible by the smallest prime factor of 210. What is the smallest such prime factor, and how many such triples exist?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.
