Q: What number must be added to the expression below to complete the square?

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-7

49-apex

An expression such as root(3) + 2 (square root of 3, added to 2) can not be simplified. Of course, you can convert the square root to a decimal and then add, to get an approximate result.

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

Five.

Related questions

Adding 100 completes the square. { I wonder why you want to complete the square when the expression already factors as x(x-20) }.

144

-3

49/4 or 12.25

-7

49-apex

An expression such as root(3) + 2 (square root of 3, added to 2) can not be simplified. Of course, you can convert the square root to a decimal and then add, to get an approximate result.

X+-7

10 + n

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

9

Five.