49/4 or 12.25
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.
You must add 1
The constant term - the part without a variable - must be equal to the square of one half the linear term - the number in front of the "x". That is, it must be (12/2)2 = 36.
I assume you mean,X2 + 12X - 5 = 0X2 + 12X = 5Now, halve the linear term (12), square it and add it to both sidesX2 + 12X + 36 = 5 + 36factor on the left, gather terms on the right(X + 6)2 = 41(X + 6)2 - 41 = 0==============vertex form.... (- 6, - 41)========================--------------vertexAnd that number added is 36
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
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.
You must add (17n + 144).