1. ALGEBRA I : SECTION 9-5 - COMPLETING THE SQUARE@
SECTION 9-5 : COMPLETING THE SQUARE

2. SOLUTION : Draw a picture.
1) Selena planted daylilies on a square piece of land with an area of 49 square feet. She wants to plant petunias around the daylilies to form a border whose area is 72 square feet. What length should she make the sides of the outer square? a
SOLUTION : Draw a picture.
daylilies x
x2 – 49 = 72
x2 = 121 x
Since length can’t be negative, the only answer that works is 11.

3. Use the square root method to solve each quadratic equation
Use the square root method to solve each quadratic equation. Remember, every quadratic equation has 2 solutions. Use
2) x2 = 49
ANSWERS : -7, 7
3) 2x2 – 300 = 0
ANSWERS :
ANSWERS : -23, 17
4) (x + 3)2 = 400

4. Quadratic Equation :
ax2 + bx + c = 0
quadratic
term
linear term
constant term

5. Solve by completing the square.
5x2 + 10x – 15 = 0
5x2 + 10x = 15 constant to one side, variables to the other.
Get the coefficient of the quadratic term to be 1
x2 + 2x = 3
Divide the coefficient of the linear term by 2, square the result, add to both sides.
x2 + 2x = 3 + 1
(x + 1) = Simplify. Make the

6. (x + 1) = 4
Take the square root of both sides.
Use when you take the square root of both sides.
x = OR x =
x = OR x = -3

7. Solve by completing the square.
5) y2 – 6y – 5 = 0
ANSWERS :
6) 5x2 – 20x – 60 = 0
ANSWERS : -2, 6
7) x2 + 8x + 8 = 0
ANSWERS :