1. The Square Root Principle & Completing the Square
Section 9.1
The Square Root Principle & Completing the Square

2. The Square Root Principle
Consider x2 = 25. What is x?
To solve equations of the form ax2 + c = d:
Isolate the squared term
Apply a square root to each side of the equation.
Remember, it can be positive or negative!

3. EX: Solve
1. k2 + 5 = 30
m2 = - 27
3. 4n = -76
4. (6h – 5)2 = 81
5. (3x – 4)2 + 1 = -80

4. To Complete the Square:
To solve ax2 + bx + c = 0
1. Divide everything by a to make the leading coefficient 1
2. Isolate the variable terms on one side.
3. Take half the coefficient of the linear term and Square it. Add that value to both sides.
4. Rewrite the left side as a binomial squared.
5. Solve.

5. EX: Solve 1. c2 – 6c + 45 = 0 2. a2 = 6a – 8 3. 4x2 = 24x + 11