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# Squares and Square Roots

# Completing the Square Exercises

### Example 1

Find the constant *c* for the following expression, assuming each expression is a square. What did we need to square to result in the expression?

*x*^{2} + 50*x* + *c*

### Example 2

Find the constant *c* for the following expression, assuming each expression is a square. What did we need to square to result in the expression?

*x*^{2} – 14*x* + *c*

### Example 3

Find the constant *c* for the following expression, assuming each expression is a square. What did we need to square to result in the expression?

*x*^{2} + 15*x* + *c*

### Example 4

*c* for the following expression, assuming each expression is a square. What did we need to square to result in the expression?

9*x*^{2} – 60*x* + *c*

### Example 5

*c* for the following expression, assuming each expression is a square. What did we need to square to result in the expression?

25*x*^{2} + 120*x* + *c*

### Example 6

Solve, or state that the equation has no real number solutions: *x*^{2} + 2*x* = 2.

### Example 7

Solve, or state that the equation has no real number solutions: *x*^{2} – 4*x* = 12.

### Example 8

Solve, or state that the equation has no real number solutions: 2*x*^{2} + 16*x* – 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: 4*x*^{2} – 4*x* + 1 = 144.