["# Simplify ( 81 + b^2 = 225 ): Step-by-Step Solution", "Solving the equation ( 81 + b^2 = 225 ) is a common algebra task that helps build foundational skills for working with quadratic expressions. This article walks you through simplifying and solving the equation step-by-step, making it easy to understand how to isolate and find the value of ( b ).", "## Step 1: Isolate the Quadratic Term", "Start with the equation:", "[
\n81 + b^2 = 225
\n]", "Subtract 81 from both sides to isolate ( b^2 ):", "[
\nb^2 = 225 - 81
\n]", "[
\nb^2 = 144
\n]", "---", "## Step 2: Solve for ( b ) by Taking the Square Root", "Now that ( b^2 = 144 ), take the square root of both sides:", "[
\nb = \pm \sqrt{144}
\n]", "[
\nb = \pm 12
\n]", "---", "## Why There Are Two Solutions", "Because squaring both a positive and negative number yields a positive result, the equation ( b^2 = 144 ) has two solutions:", "[
\nb = 12 \quad \ ext{and} \quad b = -12
\n]", "Both values satisfy the original equation when substituted back in.", "---", "## Real-World Application", "Equations like ( 81 + b^2 = 225 ) often appear in geometry, physics, or engineering contexts—such as calculating dimensions, energy values, or distances when some components are known. Solving for unknown quantities like ( b ) helps uncover missing information efficiently.", "---", "## Summary", "- Original equation: ( 81 + b^2 = 225 )
\n- Simplify: ( b^2 = 144 )
\n- Solve by taking square roots: ( b = \pm 12 )
\n- Two valid solutions reflect symmetry in squaring operations", "Understanding how to simplify and solve such equations strengthens your algebraic skills and prepares you for more advanced math challenges.", "---", "## Key SEO Keywords", "- Solve ( 81 + b^2 = 225 )
\n- Simplify quadratic equation
\n- Step-by-step solving ( b^2 = 144 )
\n- Quadratic equations for beginners
\n- How to isolate ( b^2 )
\n- Find ( b ) from ( 81 + b^2 = 225 )", "Effortlessly simplify and solve equations with this clear method—essential for students, educators, and math enthusiasts."]
