Q: X2 plus 14x equals -7 what number is added to complete the square?

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3

9

82+8 = 72

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

-7

Related questions

3

9

102 +10=110

82+8 = 72

144

-3

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

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) }.

1 is the number you are looking for.1 + 12 = 1 + 1 = 2.QED

X2 - 8X = 3halve the linear term (- 8 ), square it and add it to both sidesX2 - 8X + 16 = 3 + 16factor left, gather terms right(X - 4)2 = 19(X - 4)2 - 19 = 0-------------------------(4, - 19)----------------the vertex16 is the number that needed to be added to both sides to complete the square