Completing the Square

Question 1

steps for completing the square

Answer 1

1) rearrange the quadratic into the standard format
2) take any factors of x outside the bracket (ignore the integer for now)
3) write out the whole bracket as being squared (divide b, the number before the second x, by two; and also divide all the values by x)
4) multiply out the brackets and compare to the original
5) add or subtract the missing number to make it equal to the original

Question 2

examples of completing the square

Answer 2

x[2] + 8x + 5

(x + 4)[2]

(x + 4)[2] = x[2] + 8x + 16 (-11 to get + 5 like the orginal)

(x + 4)[2] - 11

2x[2] + 5x + 9

2(x[2] + 5/2x) + 9

2(x + 5/4)[2]

2(x + 5/4)[2] = 2x[2] + 5x + 25/8

2(x + 5/4)[2] + 47/8

Question 3

solving an equation by completing the square

Answer 3

1) complete the square first and set it equal to 0
2) rearrange the number to be on the other side
2) square root both sides - REMEMBER THE + AND -
3) rearrange to get x on its own