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Q: What number do you add to complete the square x2 plus 10x?

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You need to add -6

Twenty-Five x2 + 10x = 8 x2 + 10x + 25 = 8 + 25 (x + 5)2 = 33

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

-6

X2 + 10X - 13 = 17 add 13 to each side X2 + 10X = 30 halve the linear coefficient ( 10 ), square it and add it to both sides X2 + 10X + 25 = 30 + 25 factor on the left and gather terms on the right (X + 5)2 = 55 (X + 5)2 - 55 = 0 ---------------------------vertex form, (- 5, - 55 ), is the vertex -------------------------------------------[-------------------------------]

2x(3x + 5)

25 x2+10x-14 = 0 Completing the square:- (x+5)2-14 = 0 (x+5)2-25-14 = 0 x+5 = the sqrt of 39 x = -5-/+ the sqrt of 39

10x+10y+100 There is a common 10 in each number. 10(x+y+10)

(5x + 1)2 = 25x2 + 10x + 1

You never square a whole equation. That's just silly.

x2+10x+1 = -12+2x x2+8x+13 = 0 The solution: x = -4 + the square root of 3 or x = -4 - the square root of 3

10x - 5x + 5x = 10x

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