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Squares and Square Roots

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?

x2 + 50x + 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?

x2 – 14x + 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?

x2 + 15x + c

Example 4

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?

9x2 – 60x + c

Example 5

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?

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.

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