\[ x^2 + 144 = 169 \]

["# Solving the Equation ( x^2 + 144 = 169 ): Step-by-Step Guide", "If you're tackling the equation ( x^2 + 144 = 169 ), welcome — you're dealing with a simple but foundational algebraic problem that often appears in high school math courses. This equation models a common real-life scenario involving distances or measurement differences, making it an essential skill to master. In this SEO-optimized article, we’ll walk you through solving ( x^2 + 144 = 169 ) step by step, explain key algebraic concepts, and provide useful tips to help you understand similar equations.", "---", "## What Is the Equation ( x^2 + 144 = 169 )?", "The equation\n[\nx^2 + 144 = 169\n]\nis a quadratic equation disguised in perfect form. It involves the square of a variable ( x ), a constant term (144), and a constant result (169). To solve for ( x ), we’ll isolate ( x^2 ) and take the square root of both sides.", "---", "## Step-by-Step Solution", "### Step 1: Subtract 144 from both sides", "To eliminate the constant on the left, subtract 144 from both sides:", "[\nx^2 + 144 - 144 = 169 - 144\n]", "Simplifying gives:", "[\nx^2 = 25\n]", "---", "### Step 2: Take the square root of both sides", "Since ( x^2 = 25 ), take the square root of both sides:", "[\nx = \pm\sqrt{25}\n]", "[\nx = \pm 5\n]", "---", "## Final Answer", "[\nx = 5 \quad \ ext{or} \quad x = -5\n]", "This means the equation has two real solutions.", "---", "## Understanding the Math Behind the Solution", "Solving equations of the form ( x^2 + a = b ) relies on algebraic manipulation and understanding square roots. When isolating ( x^2 ), we reverse addition before applying the square root rule: whenever you solve ( x^2 = c ), always consider both the positive and negative roots, because both satisfy the equation.", "---", "## Real-World Applications", "This type of equation models situations where the sum of a squared quantity and a fixed value equals a constant — for example, calculating distances on a number line, solving for side lengths in geometry puzzles, or analyzing deviations in data sets.", "---", "## Tips for Solving Similar Equations", "- Always isolate the squared term by performing inverse operations.\n- Remember ( \sqrt{x^2} = |x| ), so always consider both signs.\n- Use the zero product property or square roots only after simplifying to ( x^2 = a ).\n- Verify your solution by substituting ( x = 5 ) and ( x = -5 ) back into the original equation.", "Original equation:\n[\nx^2 + 144 = 169\n]", "After simplifying:\n[\nx^2 = 25 \Rightarrow x = \pm5\n]", "---", "## Related Keywords for SEO Optimization", "- Solve ( x^2 + 144 = 169 )\n- How to solve quadratic equations step-by-step\n- Learn to isolate square terms in algebra\n- Quadratic solutions: positive and negative roots\n- Algebra tutoring for intermediate equations\n- Practice solving ( x^2 + a = b )\n- Solidify understanding of square roots and algebra", "---", "## Conclusion", "The equation ( x^2 + 144 = 169 ) is a straightforward but powerful example of solving quadratic equations algebraically. By subtracting, isolating ( x^2 ), and applying square roots, we find two solutions: ( x = 5 ) and ( x = -5 ). This process strengthens foundational algebraic skills useful in academics and real-world problem-solving. Mastering such equations enhances your ability to tackle more complex math challenges ahead.", "---", "Keywords: ( x^2 + 144 = 169 ), solve quadratic equations, algebraic steps, square root method, real solutions, algebra solutions, quadratic formula basics, math tutorial, intermediate algebra\nMeta Description: Learn how to solve ( x^2 + 144 = 169 ) with step-by-step instructions, real-life context, and tips for mastering quadratic equations in algebra. Perfect for students and self-learners."]