\( l^2 + 25 = 169 \)

["# Solving the Equation ( l^2 + 25 = 169 ): A Complete Guide", "If you’ve come across the equation ( l^2 + 25 = 169 ), you’re not alone — it’s a simple but important algebraic problem students and math enthusiasts frequently encounter. Whether you're tackling algebra for school, preparing for standardized tests, or just brushing up your math skills, understanding how to solve this equation is a valuable step.", "### What is ( l^2 + 25 = 169 )?", "This is a first-degree equation in terms of ( l^2 ), equivalently written as a quadratic equation in standard form:", "[\nl^2 + 25 = 169\n]", "The goal is to isolate ( l ) and find all real (and possibly complex) solutions.", "---", "## Step-by-Step Solution", "### Step 1: Subtract 25 from both sides\nTo solve for ( l^2 ), subtract 25 from both sides of the equation:", "[\nl^2 = 169 - 25\n]", "[\nl^2 = 144\n]", "### Step 2: Take the square root of both sides", "To isolate ( l ), take the square root of both sides:", "[\nl = \pm \sqrt{144}\n]", "[\nl = \pm 12\n]", "---", "## Final Answer", "The solutions to the equation ( l^2 + 25 = 169 ) are:", "[\n\boxed{l = 12 \quad \ ext{and} \quad l = -12}\n]", "---", "## Why Is This Equation Important?", "Solving ( l^2 + 25 = 169 ) involves key algebraic techniques: isolating variables, manipulating equations, and applying square roots. It also helps reinforce understanding of perfect squares — notice that 144 is ( 12^2 ).", "This type of equation appears in real-world applications such as physics (calculating distances or energy), engineering (error analysis), and finance (compound interest models). Mastering it builds a foundation for solving more complex equations like quadratic and radical equations.", "---", "## How to Use This Equation in Problem-Solving", "- Determine unknown lengths or quantities: Use ( l ) as a length in geometry or measurement problems.\n- Check if a solution exists: Since ( l^2 = 144 ) has real solutions, 169 is a valid right-hand side. If the equation had led to ( l^2 = -n ) (with ( n > 0 )), there would be no real solutions.\n- Practice squaring and radicals: Repeatedly practicing equations of this form strengthens number sense and algebraic fluency.", "---", "## Summary", "Solving ( l^2 + 25 = 169 ) yields two real solutions:", "[\nl = 12 \quad \ ext{and} \quad l = -12\n]", "It combines basic algebra with the concept of square roots, forming a crucial building block in advanced math. Use this guide whenever you need a clear, step-by-step breakdown of solving quadratic-style equations with constants.", "---", "# SEO Keywords:\n[ l^2 + 25 = 169, \ ext{solve } l^2 + 25 = 169, \ ext{algebra practice, solving quadratic equations, step-by-step solution to } l^2 + 25 = 169, \ ext{mathematics tuition algebra, real number solutions } l^2 + 25 = 169 ]", "---", "If you’re ready to tackle more equations, explore how to solve similar expressions and strengthen your algebraic toolkit today!"]