Solve each quadratic equation using the square root property. See Example 6. x² = 16

Verified step by step guidance

1. Recognize that the equation is already in the form \(x^2 = k\), where \(k\) is a positive number. This is ideal for using the square root property.
2. Apply the square root property, which states that if \(x^2 = k\), then \(x = \pm \sqrt{k}\). So, write \(x = \pm \sqrt{16}\).
3. Simplify the square root expression by finding the principal square root of 16, which is a perfect square.
4. Write the two possible solutions for \(x\) based on the positive and negative roots.
5. Check your solutions by substituting them back into the original equation to verify they satisfy \(x^2 = 16\).

Key Concepts

Square Root Property

The square root property states that if x² = k, then x = ±√k. This method is used to solve quadratic equations that can be written in the form x² = a constant, allowing direct extraction of the square root to find solutions.

Quadratic Equations in Standard Form

A quadratic equation typically has the form ax² + bx + c = 0. Recognizing when it can be simplified to x² = constant is essential for applying the square root property effectively.

Handling Positive and Negative Roots

When taking the square root of both sides, it is important to consider both the positive and negative roots, since both (√k)² and (-√k)² equal k. This ensures all possible solutions are found.