-7
9
9 needs to be added to complete the square. When squaring (x + n), the result is x2 + 2nx + n2. We have +10x, so n must be 10/2 = 5. Thus: (x + 5)2 = x2 +10x + 25 = x2 +10x + 14 + 9 So 9 needs to be added to complete the square, giving: x2 +10x + 14 = (x + 5)2 - 9
81. To complete the square of x^2 + 18x, you take half the coefficient of the x term (half of 18 is 9), and square that number (9 squared is 81). To confirm this works, you can now factor x^2 + 18x + 81 and see that it factors as (x+9)(x+9), or (x+9)^2, a perfect square.
You need to add -22.
144
-3
49/4 or 12.25
-7
Adding 100 completes the square. { I wonder why you want to complete the square when the expression already factors as x(x-20) }.
9
9
You must add 36 to complete the square on the left hand side.You must add 36 to complete the square on the left hand side.You must add 36 to complete the square on the left hand side.You must add 36 to complete the square on the left hand side.
9 needs to be added to complete the square. When squaring (x + n), the result is x2 + 2nx + n2. We have +10x, so n must be 10/2 = 5. Thus: (x + 5)2 = x2 +10x + 25 = x2 +10x + 14 + 9 So 9 needs to be added to complete the square, giving: x2 +10x + 14 = (x + 5)2 - 9
You must add 1
62
x2 + 5x + 6¼ = (x + 2½)2 and, hence, is a perfect square. As the co-efficient of x2 (the first term) is 1, you can safely follow this rule: Add the square of half the co-efficient in the second term, in order to complete the square. In this case, you take half of 5 (which is 2½) and, then, square it. This gives you your 6¼.