Completing the Square Exercises

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

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

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

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

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

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

x² + 2x = 2

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

x² – 4x = 12

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

2x² + 16x – 18 = 0

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

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

4x² – 4x + 1 = 144