\[ a^2 + 25 = 169 \] - Dygne

["Solve the Equation ( a^2 + 25 = 169 ) – Step-by-Step Guide", "Solving algebraic equations is a fundamental math skill, and understanding how to isolate variables like ( a ) in expressions such as ( a^2 + 25 = 169 \ is essential for students and enthusiasts alike. In this article, we’ll walk through how to solve the equation ( a^2 + 25 = 169 ) clearly and efficiently.", "---", "### Understanding the Equation", "Start with the simple equation:", "[
\na^2 + 25 = 169
\n]", "Our goal is to find the value(s) of ( a ) that make this true. First, isolate ( a^2 ) by subtracting 25 from both sides:", "[
\na^2 = 169 - 25
\n]", "[
\na^2 = 144
\n]", "---", "### Solving for ( a )", "Now that ( a^2 = 144 ), take the square root of both sides to solve for ( a ). Remember, taking the square root introduces both positive and negative solutions:", "[
\na = \pm\sqrt{144}
\n]", "[
\na = \pm12
\n]", "---", "### Final Answer", "Thus, the solutions are:", "[
\na = 12 \quad \ ext{or} \quad a = -12
\n]", "These are the two values that satisfy the original equation ( a^2 + 25 = 169 ).", "---", "### Verification", "To confirm, substitute back into the original equation:", "- For ( a = 12 ):
\n ( 12^2 + 25 = 144 + 25 = 169 ) ✅
\n- For ( a = -12 ):
\n ( (-12)^2 + 25 = 144 + 25 = 169 ) ✅", "Both solutions are correct.", "---", "### Why This Equation Matters", "Equations like ( a^2 + 25 = 169 ) are building blocks for more advanced math—quadratic equations, graphing parabolas, solving real-world problems, and beyond. Mastering this type of problem enhances algebraic fluency and prepares learners for higher-level math topics.", "---", "### Tips to Solve Similar Equations", "- Always isolate the variable’s square by performing inverse operations.
\n- Remember that squaring a number yields a positive result—so always consider both positive and negative roots.
\n- Always check your solutions by substituting back into the original equation.", "---", "### Related Keywords for SEO Optimization", "To boost this article’s visibility, include these SEO keywords naturally:", "- Solve ( a^2 + 25 = 169 <br/>\n- Step-by-step quadratic equation
\n- How to solve ( a^2 = 144 <br/>\n- Find value of ( a ) in ( a^2 + 25 = 169 <br/>\n- Algebraic equation solutions
\n- Simple quadratic equations for beginners
\n- Teach math, algebra problem solving", "---", "By understanding and practicing this straightforward equation, you build confidence in algebra—key to unlocking more complex mathematical challenges ahead. If you found this guide helpful, share it and explore more math tutorials tailored for learners at every level.", "---", "References & Further Reading:
\n- Khan Academy Algebra
\n- Algebra fundamentals for students
\n- How to solve quadratic equations step-by-step", "---", "Stay curious and keep solving equations!"]