\[ c^2 = 81 + 144 \]

["# Solving ( c^2 = 81 + 144 ): A Simple Step-by-Step Guide", "Understanding how to solve an equation like ( c^2 = 81 + 144 ) is a fundamental skill in algebra that applies to many areas of mathematics and real-world problem solving. In this article, we’ll explore how to simplify and solve this equation step by step, provide key mathematical insights, and demonstrate why mastering such problems is valuable.", "## What Equation Are We Solving?", "The equation is:\n[ c^2 = 81 + 144 ]", "At first glance, it appears simple, but understanding how to break it down helps build stronger problem-solving habits.", "## Step 1: Simplify the Right-Hand Side", "Begin by performing the addition on the right side of the equation:\n[ c^2 = 81 + 144 = 225 ]", "So, ( c^2 = 225 ). This simplification removes unnecessary complexity and focuses on solving for ( c ).", "## Step 2: Solve for ( c ) by Taking the Square Root", "To isolate ( c ), take the square root of both sides:\n[ c = \pm\sqrt{225} ]", "Since ( 15 \ imes 15 = 225 ), we have:\n[ c = \pm 15 ]", "This means ( c = 15 ) or ( c = -15 ).", "## Why This Equation Matters", "- Square Roots & Real-World Applications: This type of equation appears in geometry (e.g., calculating side lengths), physics, and engineering.\n- Positive and Negative Solutions: Understanding that solutions can be positive or negative is crucial in modeling real scenarios where direction or magnitude matters.\n- Foundational Algebra: Solving quadratic-like equations like ( c^2 = k ) lays the groundwork for manipulating quadratic equations, discriminants, and function graphs.", "## Final Answer", "The full solution to the equation ( c^2 = 81 + 144 ) is:\n[ c = \pm 15 ]", "---", ".Key Takeaways:\n- Simplify constants before solving.\n- Apply square roots carefully, remembering both positive and negative solutions.\n- Practicing such equations strengthens algebraic fluency and logical reasoning.", "For more help with solving equations and algebraic principles, explore our complete guides on quadratic equations, square roots, and solving for variables.", "---", "Keywords: solve ( c^2 = 81 + 144 ), algebraic equation solution, simplify ( c^2 = 225 ), take square root, real number solutions, algebra practice, how to solve quadratic-like equations, step-by-step math tutorial."]