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Pani-rosa [81]
3 years ago
10

Twelve more than half of a number is equal to the number

Mathematics
1 answer:
tester [92]3 years ago
5 0
Let's consider that number to be 'x'..
So, twice the number (2x) is 12 greater than than the half of the number.
So the equation will be like,
2x=12+x/2
Solving this further,
2x=(24+x)/2
=> 4x=24+x
=>4x-x=24
=>3x=24
=>x=8..
So the number is "8".
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What constant do you need to add to each quadratic to complete the square? 1. x2 - 4x = 0 4 2. x2 - 8x = 6 9 3. 3x2 + 18x = 24 1
Radda [10]
1) You must add 4 to each side to complete the square.
2) You must add 16 to each side to complete the square.
3) You must add 27 to each side to complete the square.

Explanation:
1) x²-4x=0
To find the number that we add to both sides, we look at b, the cofficient of x.  It is -4. We divide it by 2 and square it; -4/2 = -2; (-2)² = 4.  This is the value that we add to both sides.

2) x²-8x=6
-8/2 = -4; (-4)²=16
We add 16 to each side to complete the square.

3) 3x²+18x=24
First we can factor a 3 out of the left side:
3(x²+6x) = 24
Our b value is now 6.  6/2 = 3; 3²=9.  The 9 would, however, go in the parentheses, so it would be multiplied by 3, which makes 27; this means we would add 27 to both sides.
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