Completing the Square

Complete the Square
x² + 6x = 5

• (x + 3)² = 5

• (x + 6)² = 9

• (x + 3)² = 14

• (x + 6)² = 14

What is the first step to complete the square for this quadratic equation?

2y² + 20y + 18 = 0

• factor the LEFT

• divide by 2

• subtract 18 from both sides

• add a blank/box to both sides

Give the reason for each step in the following solution of an equation by using the

Square Root Property.

• Factor the perfect square trinomial.

• Square Root Property

• Rewrite as two equations.

• Solve each equation.

What are the steps to solving this by completing the square?

• Subtract 21 from both sides of the equation

• Add 25 to both sides of the equation

• Rewrite the left hand side as a (binomial)²

• Take the square root of both sides of the equation

• Subtract 5 from both sides of the equation

What is the first step to solving THIS equation by completing the square?
a² + 10a + 21 = 0

• Set the equation equal to zero

• Divide 10 by 2 and add the result to both sides

• Add a² and 10a together

• Subtract the 21

• x = -1 + i√5

• x = -1 ± i√5

• x = -1 - i√5

• x = 2 + i√5

Find the value of c that makes each trinomial a perfect square. ( x² + 26x + c )

Complete the square.
x² + 6x + ____

• x² + 6x + 9

• x² + 6x - 36

• x² + 6x + 36

• x² + 6x - 9

Complete the square.
x² + 14x + ____

• x² + 14x - 196

• x² + 14x + 49

• x² + 14x - 49

• x² + 14x + 196