The quadratic equation formula, what I'll call QEF, is used to solve for the values of x in a quadratic equation that has the form y = a(x squared) + bx + c. Other methods for solving exist, such as factoring into binomials and completing the square for simpler equations, but the QEF can be used for all quadratic equations. First, it's helpful to realize that all quadratic equations have two possible solutions or answers. Sometimes those solutions happen to be "twins", as in the case where, for example, x equals 7 and x equals 7. However, a more typical answer would be something like x equals 5 and x equals 3. From the form above, y = a(x squared) + bx + c, a is the coefficient or number right next to x squared, b is the coefficient or number next to x, and c is the number by itself. After examining the quadratic equation that you need solutions for, it would be helpful to write the values of a, b, and c before using them in the QEF. Perhaps the easiest way to show how to use the QEF is to do an example. I'll make up a quadratic equation y = 2(x squared) + 3x - 5. Therefore, I'll write a=2, b=3, and c= - 5. What you have written for the QEF x=-b+-sqrt b2-4ac/2a is correct, but I'll do the solution in steps instead of all at once. STEP 1. Square the value of "b", so 3 squared is 3X3=9. STEP 2. Next, multiply -4 times the value of "a" times the value of "c", so -4 X 2 X -5 = 40. STEP 3. Add the results from Steps 1 and 2 above, so 9 + 40=49. STEP 4. Take the square root of your result from Step 3. Sometimes the result is a whole number, and other times it is best to use your result in the square root symbol. In our example, the square root of 49 is a whole number, 7. STEP 5. Multiply 2 times the value of "a", so 2X2=4. STEP 6. Find the opposite value of "b", so -b = -3. STEP 7. Find the following two values. ADD the results for Steps 6 and 4, so -3 + 7 = 4. Next, SUBTRACT the result from Step 4 from the result for Step 6, so -3 - 7 = -10. STEP 8. Almost done! To get your first answer, take the FIRST result from Step 7 and divide it by the result from Step 5, so 4 divided by 4 is 1. STEP 9. Finally, to get your second answer, take the SECOND result from Step 7 and divide it by the result from Step 5, so -10 divided by 4 is the fraction -10/4 or -5/2 in simplified form. You can do all the steps together if you know how to effectively use parentheses in a calculator. Otherwise, the steps above will work. Our final two solutions or answers are x equals 4/5 and x equals -2.

Using addition with regrouping worksheets is a useful way to add more than two numbers. Line up three numbers in a column and add them in the same order. For example, if you have a sum of 21 and a tens sum of 32, you would add the first two numbers in the ones column and then carry over the other two to the tens column to get 81. This regrouping technique works with any question involving two digits and any place value.

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