Completing the Square

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Algebra

After watching the video on this concept, take this quiz to see how much you've learned! See the results right when you're done, AND, there's even an option to send the results to an email of your choice. Good luck, no pressure, and YAY MATH!

Would you like to share this quiz with others who, like you, whisper to equations, "You... complete... my square"? Here is the shortened link: https://forms.gle/baCzLpUthW7VMkcD8

What's your name? *

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(If you want your score automatically sent to you or to someone else, which email would you like to use? This is optional and for your convenience; everything is kept private.)

What must be the value of the leading coefficient whenever completing the square? *

(Meaning, what must the coefficient "a" that's in front of x², be equal to?)

1 point

What is the following step in each of the completing the squares problems below?

x² + 14x – 15 = 0 *

1 point

Adding 15 to both sides

subtracting 14x from both sides

Factoring out an x from the left side

Prime

x² + 6x = –8 *

1 point

Add 8 to both sides.

Half the second term (6) which becomes 3, and square the result (3² = 9), add to both sides.

Half the first term (1) which becomes ½, and square the result ((½)² = (¼)), add to both sides.

Factor out 2.

Cry. Needlessly though, because completing the square is great.

Please solve by completing the square:

x² − 12x + 11 = 0 *

1 point

x = 3, x = 6

x = 12

x = 0

x = 1, x = 11

a² − 10a + 26 = 8 *

1 point

Completing the square doesn't work here.

a = –2, a = 12

a = 4 ± √5

a = 4, a = 5

a = 5 ± √7

2x² = –6 + 8x *

Hint: First reorder equation, then divide the GCF before completing the square.

1 point

No solution

x = 1, x = 3

x = 5

x = 3

x = 0

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