-10
y=x2-18x+52First off, this does not factor cleanly, but even if it did it would not help us. We must complete the square to yield a perfect-square trinomial (a trinomial that can be written in the form (x-a)2 where a is a real number.To do this, halve the coefficient of the single-x term (for this case, the term 18x) and square it.18/2=992=81The result of this process can be added to the two terms involving x to get a perfect square trinomial. For instance, the trinomial that would result would be:x2-18x+81=(x-9)2However, there is already 52 of that 81 that is needed present, so in reality, you only need to add 29 (81-52=29) to the right side of the equation to get a perfect-square trinomial. Whatever is done to one side of the equation must be done to the other side, so since you added 29 to the right side, you must add 29 to the left side, giving you:y+29=x2-18x+52+29y+29=x2-18x+81y+29=(x-9)2y=(x-9)2-29This is in vertex form, you can see that the vertex is at (9,-29)
Sqrt of 453664 is 672 and a bit.So next square is 673 squared, ie 452929, so 265 must be added.
144
96 + 4 = 100 96 + 25 = 121 96 + 100 = 196 96 + 529 = 625
Oh, dude, to make 3000 a perfect square, you'd need to add the square of the nearest whole number to its square root, which is 55. So, the least number you'd have to add is 55 squared, which is 3025. But hey, who's counting, right?
12
A perfect square trinomial is looking for compatible factors that would fit in the last term when multiplied and in the second term if added/subtracted (considering the signs of each polynomials).* * * * *A simpler answer is: write the trinomial in the form ax2 + bx + c. Then, if b2 = 4ac, it is a perfect square.
2 1/4
There are no FOLLOWING constants! The answer is 0.25
5
5607 + 18 = 5625, a perfect square. The perfect square of a square root is the number you started with.
(Y2 + Y) added to (Y + 1) will always give a perfect square [of (Y + 1)2].
y=x2-18x+52First off, this does not factor cleanly, but even if it did it would not help us. We must complete the square to yield a perfect-square trinomial (a trinomial that can be written in the form (x-a)2 where a is a real number.To do this, halve the coefficient of the single-x term (for this case, the term 18x) and square it.18/2=992=81The result of this process can be added to the two terms involving x to get a perfect square trinomial. For instance, the trinomial that would result would be:x2-18x+81=(x-9)2However, there is already 52 of that 81 that is needed present, so in reality, you only need to add 29 (81-52=29) to the right side of the equation to get a perfect-square trinomial. Whatever is done to one side of the equation must be done to the other side, so since you added 29 to the right side, you must add 29 to the left side, giving you:y+29=x2-18x+52+29y+29=x2-18x+81y+29=(x-9)2y=(x-9)2-29This is in vertex form, you can see that the vertex is at (9,-29)
Sqrt of 453664 is 672 and a bit.So next square is 673 squared, ie 452929, so 265 must be added.
21
Because numbers are infinite, there is an infinite number of answers. e.g. What number should be added to 2 to make a perfect square? 2+2=4 (a perfect square) 2+7=9 (a perfect square) 2+14=16 (a perfect square) 2+23=25 (a perfect square) etc... Did you have a specific number in mind.
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