x2 + 12x - 11 = x2 + 12x + (12/2)2 - (12/2)2 - 11
= (x + 6)2 - 47
x2 + 8x - 2 = 0 => x2 + 8x = 2 => x2 + 8x + 16 = 2 + 16 = 18 => (x + 4)2 = 18 => x + 4 = +or- sqrt(18) = +or- 3*sqrt(2) so x = -4 +or- 3*sqrt(2)
(x-y)2 is a square so (x-y)2 >= 0 expanding, x2 - 2xy + y2 >= 0 so x2 + y2 >= 2xy or 2xy <= x2 + y2
x2+6x-7 = 0 (x+3)2-7 = 0 (x+3)2-7-9 = 0 (x+3)2 = 16 x+3 = + or - 4 x = - 3 + or - 4 x = 1 or -7
144
Twenty-Five x2 + 10x = 8 x2 + 10x + 25 = 8 + 25 (x + 5)2 = 33
ask jesus.
(x+8)^2=105
No because the discriminant of the given quadratic expression is less than zero.
X2+11x+11 = 7x+9 X2+11x-7x+11-9 = 0 x2+4x+2 = 0 Solve as a quadratic equation by using the quadratic equation formula or by completing the square: x = -2 + or - the square root of 2
y = x2 - 6x + 2 y = x2 - 6x + 9 - 7 y = (x - 3)2 - 7
x2 + 6x = 7 ⇒ x2 + 6x + 9 = 7 + 9 ⇒ (x + 3)2 = 16 ⇒ x + 3 = ±4 ⇒ x = -7 or 1
x2 + 20x +0 =30 [(20/2)2 =100] x2 + 20x + 100 =30 +100 √(x+10)2=√130 x+10=√130 x= −10+√130 √ means square root
Since there are only terms in x2 and constants, but none in x, completing the square is not an option! x2 - 14 = 7 x2 = 21 and so x2 = sqrt(21)
Plus or minus the base. If the base is X and you square it, you get X2. If you take the square root of that, you get Plus or Minus X. This is because X*X equals X2 and -X*-X also equals X2.
No.
If you aren't dealing with algebra, such as x2+3x+21, then completing the square wont be able to solve the porblem, however if you are using algebra, and you cannot factorise, then completing the square will always work
the problem is not proper to slove. I just want to suggest to follow the related link that explains the concept of completing the square clearly.