Solve a quadratic equation using square roots

Learning Objectives Identify quadratic equations that can be solved using the square root property. Correctly isolate the squared term in a quadratic equation. Apply the square root property to solve for the variable, including both positive and negative roots. Simplify radical expressions that arise in solutions. Determine whether a quadratic equation has two real solutions, one real solution, or no real solutions based on the square root property. Solve equations of the form a(x-h)^2 = k. Model and solve real-world problems using this method. If you drop a rock from a 100-meter cliff, how long does it take to hit the ground? 🧗 This is a question you can answer precisely using the square root method for quadratic equations! This tutorial focuses on a direct and efficien...

TermDefinitionExample Quadratic EquationAn equation that can be written in the standard form ax^2 + bx + c = 0, where 'a' is not equal to 0. This method works best when b = 0.3x^2 - 75 = 0 is a quadratic equation where b = 0. Square Root PropertyA property stating that if a squared expression equals a non-negative number, then the expression itself is equal to both the positive and negative square root of that number.If x^2 = 49, then the Square Root Property tells us that x = 7 or x = -7. Isolate the Squared TermThe process of using inverse operations to get the term containing the exponent (like x^2 or (x-3)^2) alone on one side of the equation.In 2x^2 - 18 = 0, you would add 18 and then divide by 2 to isolate x^2. RadicalThe symbol (√) used to denote the principal (non-negati...

The Square Root Property If x^2 = k, then x = ±√k This is the fundamental rule for this method. After you have isolated the squared variable, you take the square root of both sides. It is critical to remember the 'plus or minus' (±) symbol, as there are typically two solutions. Solving Equations of the Form ax^2 + c = 0 x = ±√(-c/a) This is a direct application of the Square Root Property. First, subtract 'c' from both sides. Second, divide both sides by 'a'. Finally, apply the Square Root Property to the result. Solving Equations of the Form a(x-h)^2 = k x = h ± √(k/a) For equations where a binomial is squared (vertex form). First, divide both sides by 'a'. Second, apply the Square Root Property. Finally, add 'h' to...