Algebra 101 - Unit 6

Lesson 34: Solving Quadratics by Square Roots

Some quadratic equations can be solved by taking the square root of both sides. This method works when the equation is in the form ax² + c = 0 or can be rewritten in that form.

Steps to Solve by Square Roots

1. Isolate the x² term on one side of the equation.
2. Take the square root of both sides.
3. Remember to include both the positive and negative roots (±).
4. Solve for x.

Examples

Example 1: Solve x² = 25

1. Take the square root: x = ±√25
2. Solution: x = ±5

Example 2: Solve 3x² − 12 = 0

1. Isolate x²: 3x² = 12 → x² = 4
2. Take the square root: x = ±√4
3. Solution: x = ±2

Example 3: Solve (x − 3)² = 16

1. Take the square root: x − 3 = ±√16 → x − 3 = ±4
2. Solve each case: x = 3 + 4 = 7 or x = 3 − 4 = −1

Practice Problems

1. Solve x² = 36
2. Solve 5x² = 20
3. Solve (x + 2)² = 9
4. Solve 2x² − 18 = 0
5. Solve (3x − 1)² = 25