a2 Completing the square--converting to easy

a2 Completing the square--converting to easy

Open Ended

The problem x² + 4x - 7 = 0 is "easy" to solve by completing the square because:

So the problem 5x² + 3x - 7 = 0 is "not easy" to solve because:

• 5x² is not a perfect square

• the 3 in front of the 3x is odd, so you will get a fraction if you split it into 2 equal pieces

Poll

What number should we multiply 5x² by to "create" a perfect square?

• 3

• 4

• 5

• 7

Multiple Choice

If we multiply the polynomial equation 5x² + 3x - 7 = 0 by 5, the resulting polynomial equation will be:

• 25x² + 3x - 7 = 0

• 25x² + 15x - 7 = 0

• 25x² + 15x - 35 = 0

• 25x² + 15x - 35 = 5

Poll

What number should we multiply the polynomial 25x² + 15x - 35 = 0 by to preserve the square first term, but create an even middle term?

• 2

• 3

• 4

• 5

Multiple Choice

If we multiply the polynomial equation 25x² + 15x - 35 = 0 by 4, the resulting polynomial equation will be:

• 100x² + 12x - 28 = 0

• 100x² + 60x - 140 = 0

• 25x² + 60x - 35 = 0

• 25x² + 60x - 140 = 0

Multiple Choice

To solve, you would rewrite as 100x² + 70x + ____ = 140 + ____. What would your box look like?

Multiple Choice

To solve, you would rewrite as 100x² + 70x + ____ = 140 + ____. What would your finished box look like?

Fill in the Blanks

To solve, you would fill in the blanks with 9 and have,

100x² + 70x + 9 = 140 + 9. Then you would rewrite it as a perfect

square binomial. What would the rewritten problem look like?

(10x + 3)² = 149

Multiple Select

What would your next steps include in solving the equation

(10x + 3)² = 149

Check all that apply:

• Take the square root of both sides

• add a +/- in front of the square root of 149

• subtract 3 from both sides

• add 10 to both sides

Multiple Choice

What would the final solutions to the equation

(10x + 3)² = 149

be:

Open Ended

Reflect on what you learned from completing this lesson.

What did it solidify in your learning?

How did you like the format?

How could it have been improved?