\[ a^2 + 64 = 100 \] - Verified Servers

["# Solve the Equation ( a^2 + 64 = 100 ): A Step-by-Step Guide", "Solving algebraic equations is a foundational skill in mathematics, and understanding how to solve expressions like ( a^2 + 64 = 100 ) is essential for students, educators, and math enthusiasts alike. If you’ve come across the equation ( a^2 + 64 = 100 ) and are wondering how to find the value of ( a ), this complete guide explains everything you need to know.", "## Understanding the Equation", "The equation ( a^2 + 64 = 100 ) involves a squared variable and constant terms. The goal is to isolate the variable ( a ) and determine its possible values.", "## Step-by-Step Solution", "### Step 1: Isolate the squared term", "Start by subtracting 64 from both sides of the equation:", "[
\na^2 + 64 - 64 = 100 - 64
\n]", "[
\na^2 = 36
\n]", "### Step 2: Solve for ( a ) by taking the square root", "To find ( a ), take the square root of both sides. Remember, taking the square root yields both the positive and negative roots:", "[
\na = \pm\sqrt{36}
\n]", "[
\na = \pm 6
\n]", "## Solutions", "The equation ( a^2 + 64 = 100 ) has two real solutions:", "- ( a = 6 )
\n- ( a = -6 )", "## Why This Matters", "Understanding how to solve such equations strengthens algebraic problem-solving skills. These skills are crucial in higher-level mathematics, physics, engineering, computer science, and economics. Moreover, mastering equation-solving helps students develop logical thinking and precision.", "## Real-World Applications", "While ( a^2 + 64 = 100 ) is a simple algebraic equation, similar forms appear in real-life scenarios—such as calculating distances, optimizing financial models, or analyzing quadratic functions that describe projectile motion or profit curves.", "## Additional Tips", "- Always verify your solutions by substituting back into the original equation.
\n- Remember that squaring both sides of equations requires caution—always check for extraneous solutions.
\n- Practice similar equations to build confidence and speed.", "## Conclusion", "Solving ( a^2 + 64 = 100 ) is straightforward but reinforces key mathematical principles. By isolating the variable and applying square root properties, you determine ( a = \pm 6 ). This simple equation opens the door to deeper algebraic understanding and real-world applications—making it a vital concept in mathematics education.", "---", "Keywords: ( a^2 + 64 = 100 ), solving quadratic equations, isolate variable, square root, algebra tutorial, equation solving, math practice problems.
\nMeta Description: Learn how to solve ( a^2 + 64 = 100 ) step-by-step. Discover the solutions ( a = \pm 6 ), history, tips, and real-world applications. Perfect for students and math learners."]