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.
What must be added to x²+5x to make a perfect square please help me to solve it and please show the working please I am begging you please 🙏 help me
62
5607 + 18 = 5625, a perfect square. The perfect square of a square root is the number you started with.
4
-17
The idea is to take half the linear part (12, in this case), then square it. The constant part must be equal to this result.
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
5607 + 18 = 5625, a perfect square. The perfect square of a square root is the number you started with.