The Square Root
Principle &
Completing the
Square
 Consider
 To



x2 = 25.
What is x?
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!
1.
2.
3.
4.
5.
k2 + 5 = 30
- 2 m2 = - 27
3
32
4n2 + 20 = -76
(6h – 5)2 = 81
(3x – 4)2 + 1 = -80
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.

1.
c2 – 6c + 45 = 0
2. a2 = 6a – 8
3. 4x2 = 24x + 11
4. 2x2 - 5x – 12 = 0