its 1/4
(x-1/2)²= x²-21/2x+1/4= x²-x+1/4
for -Apex
49-apex
-7
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.
To complete the square for the expression (x^2 + 12x - 6), we need to focus on the (x^2 + 12x) part. We take half of the coefficient of (x) (which is 12), square it, and add it to both sides. Half of 12 is 6, and squaring it gives us 36. Therefore, we must add 36 to both sides of the equation.
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
Adding 100 completes the square. { I wonder why you want to complete the square when the expression already factors as x(x-20) }.
-3
144
49-apex
-7
49/4 or 12.25
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.
To complete the square for the expression (x^2 + 12x - 6), we need to focus on the (x^2 + 12x) part. We take half of the coefficient of (x) (which is 12), square it, and add it to both sides. Half of 12 is 6, and squaring it gives us 36. Therefore, we must add 36 to both sides of the equation.
10 + n
X+-7
9
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