First, square both sides of the given equation:
["Title: Mastering Algebra: First, Square Both Sides of an Equation", "In algebra, solving equations often requires clever manipulations to isolate variables. One powerful technique is squaring both sides of an equation—this transformation is frequently used to eliminate square roots, simplify expressions, and solve equations that initially appear complex. Whether you're simplifying expressions or solving nonlinear equations, knowing how and when to square both sides can greatly improve your problem-solving skills.", "### What Does it Mean to Square Both Sides?", "Squaring both sides of an equation means multiplying each side by itself. For example, if the equation is:", "[\n\sqrt{x + 3} = 5\n]", "Squaring both sides gives:", "[\n(\sqrt{x + 3})^2 = 5^2 \Rightarrow x + 3 = 25\n]", "This eliminates the square root, turning the equation into a simpler linear form. However, because this operation isn't one-to-one (both positive and negative numbers squared yield the same result), squaring introduces the risk of extraneous solutions—solutions that satisfy the transformed equation but not the original one. Always verify your answers!", "### When to Square Both Sides", "Squaring both sides is especially useful when:", "- Your equation contains square roots that you want to eliminate.\n- You need to eliminate exponents to reduce the equation to a solvable polynomial.\n- You’re working with equations like $ a = \sqrt{b} $, where isolating the root isn’t straightforward.", "For example:", "[\n2x - 1 = \sqrt{x + 5}\n]", "Squaring both sides yields:", "[\n(2x - 1)^2 = (\sqrt{x + 5})^2\n\Rightarrow 4x^2 - 4x + 1 = x + 5\n]", "Now you can solve the resulting quadratic equation using standard methods.", "### Step-by-Step: How to Square Both Sides", "1. Isolate the radical (if present) — though not always necessary, isolating helps avoid mistakes.\n2. Square each side of the equation.\n3. Simplify both sides into a single equation (often polynomial).\n4. Solve using algebraic techniques.\n5. Check solutions in the original equation to discard extraneous ones.", "### Why Verify Solutions?", "Because squaring both sides doubles the solution set, some values that appear valid algebraically may violate the original equation’s domain or sign conditions. For instance, $ \sqrt{x} = -3 $ has no real solution, yet squaring gives $ x = 9 $, which fails in the original equation.", "### Common Pitfalls", "- Forgetting to check for extraneous solutions.\n- Assuming squared equations are always equivalent to the original.\n- Incorrectly simplifying after squaring, especially with sums or differences.", "### Conclusion", "Squaring both sides is an essential algebraic tool for simplifying and solving equations involving roots. When used carefully—paired with verification—this method unlocks solutions to otherwise tricky problems. Practice identifying when and how to apply squaring to build deeper mastery of algebraic manipulation.", "---", "Keywords: square both sides, algebra techniques, solving equations, eliminate square roots, extraneous solutions, algebraic manipulation, quadratic equation, linear equation solving, mathematical methods.", "Meta Description: Learn how to square both sides of an equation to simplify and solve algebraic expressions. Discover steps, best practices, and pitfalls like extraneous solutions. Master key algebra techniques today.", "---", "Transform your algebra skills—start by squaring both sides, then verify, and watch your problem-solving confidence grow!"]
