Free Math & Algebra Help

One of the most asked questions in algebra class is "How do you complete the square in a math problem?" Completing the square seems to be one of the most difficult tasks in an algebra class, but it is actually fairly easy if you remember a series of steps. The steps are shown below:

Solve 2x² + 3x - 8 = 0 by completing the square.

Step 1 - Isolate the x-squared and x-terms on one side of = .

Step 2 - Divide all terms on both sides by the coefficient on x² . In this case divide by 2. Simplify the result. 


Step 3 - Take 1/2 of the coefficient of the x-term. Square this amount and then add this result to both sides of the equation. Simply the sum on the right side of =.

1/2 of 3/2 = 1/2 * 3/2 = 3/4
(3/4)² = (3/4)*(3/4) = 9/16

x² + (3/2)x + 9/16 = 4 + 9/16

x² + (3/2)x + 9/16 = 64/16 + 9/16

x² + (3/2)x + 9/16 = 73/16

Step 4 - Factor the left side of the equation. Write in perfect square form.

(x + 3/4)(x + 3/4) = 73/16 which may be written as
(x + 3/4)² = 73/16

Step 5 - Solve this equation by extracting square roots. This amounts to taking the square root of both sides and applying a +/- sign to the radical.

The printable table shown below is available at Free Printable Multiplication Times Tables and from this page you may print out all the blank tables you want, with answers, and/or without answers. Also, on this page there are examples of how these tables have been used with a struggling arithmetic student.

This is how you use these multiplication times tables: Randomly ask multiplication facts. As the student correctly answers the questions, strike out the fact. If the student misses the problem, circle it. After one time through, you will see patterns. The student might have problems with multiples of 7. So you have them write out their multiples of 7 a few times. Also, you stress the commutative property: 7x5 = 5x7. . . it is amazing how many beginning arithmetic students do not realize this! Another thing to do is skip the multiples that the student already has down pat. So for example, if they have their multiples of 5 down, draw a line through those multiples and skip them. This gives you more time to focus on what needs to be practiced using these free multiplication worksheets.

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