Solve a quadratic equation using square roots

Learning Objectives Identify quadratic equations that can be solved using the square root property. Isolate the squared term in a quadratic equation using inverse operations. Apply the square root property to find all possible solutions. Solve quadratic equations that result in two real solutions, including rational and irrational numbers. Solve quadratic equations that result in a single, repeated real solution. Solve quadratic equations that result in two complex solutions using the imaginary unit 'i'. How long would it take a dropped object to fall from the top of a 100-meter cliff? 🧗 The answer lies in a special type of quadratic equation you can solve in just a few steps! This tutorial focuses on the square root property, a powerful and direct method for sol...

TermDefinitionExample Quadratic EquationAn equation that can be written in the standard form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.The equation 4x² - 9 = 0 is a quadratic equation where a=4, b=0, and c=-9. This type is ideal for solving with square roots. Square Root PropertyA principle stating that if a squared expression equals a constant, then the expression itself is equal to the positive and negative square root of that constant.If x² = 25, the Square Root Property tells us that x = ±√25, so x = 5 or x = -5. Isolating the Squared TermThe process of using inverse operations to get the part of the equation that is being squared (like x² or (x-2)²) by itself on one side of the equal sign.In 3(x-1)² - 12 = 0, you would add 12 and then divide by 3 to isolate (x-1)²,...

The Square Root Property If X² = k, then X = \pm\sqrt{k} This is the fundamental rule for this method. After isolating the squared expression (X), you take the square root of the constant (k) on the other side. The '±' is critical as it accounts for both possible solutions. Square Root of a Negative Number For any positive real number k, \sqrt{-k} = i\sqrt{k} When the constant 'k' is negative, this rule allows you to express the solution using the imaginary unit 'i'. This is how you find complex solutions.