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Completing the Square Exercises

Example 1

Find the constant c for the following expression, assuming it's a perfect square. What did we need to square to result in the expression?

x2 + 50x + c

Example 2

Find the constant c for the following expression, assuming it's a perfect square. What did we need to square to result in the expression?

x2 – 14x + c

Example 3

Find the constant c for the following expression, assuming it's a perfect square. What did we need to square to result in the expression?

x2 + 15x + c

Example 4

Find the constant c for the following expression, assuming it's a perfect square. What did we need to square to result in the expression?

9x2 – 60x + c

Example 5

Find the constant c for the following expression, assuming it's a perfect square. What did we need to square to result in the expression?

25x2 + 120x + c

Example 6

Solve, or state that the equation has no real number solutions:

x2 + 2x = 2

Example 7

Solve, or state that the equation has no real number solutions:

x2 – 4x = 12

Example 8

Solve, or state that the equation has no real number solutions:

2x2 + 16x – 18 = 0

Example 9

Solve, or state that the equation has no real number solutions:

Example 10

Solve, or state that the equation has no real number solutions:

4x2 – 4x + 1 = 144