SOLUTION: How do I solve the sum of twice a number and its square is 143? I can write out the equation, but I don't know the answer.

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Question 281519: How do I solve the sum of twice a number and its square is 143? I can write out the equation, but I don't know the answer.
Found 2 solutions by Mathematicians, JBarnum:
Answer by Mathematicians(84) About Me  (Show Source):
You can put this solution on YOUR website!
Judging by your question, writing out the equation is:
2x+%2B+x%5E2+=+143
In order to solve this equation, you need to get everything on one side:
x%5E2+%2B+2x+-+143+=+0
We need to find two numbers that add up to be positive 2 and multiply to be 143. 143 is 13 * 11 which is a coincidence because those are two apart from each other.
We get
%28x+%2B+13%29%28x+-+11%29+=+0
Using zero product principle, we know that
%28x+-+11%29+=+0
highlight+%28x+=+11%29
or
%28x+%2B+13%29+=+0
highlight+%28x+=+-13%29

Both of these are your answers! See ya around!

Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
2x%2Bx%5E2=143 this is a quadratic equation , set it equal to 0
x%5E2%2B2x-143=0 a=1 b=2 c=-143
-b%2B%28%28sqrt%28b%5E2-4ac%29%29%2F2a%29-b-%28%28sqrt%28b%5E2-4ac%29%29%2F2a%29
-2%2B%28%28sqrt%282%5E2-4%2A1%2A-143%29%29%2F%282%2A1%29%29 -2-%28%28sqrt%282%5E2-4%2A1%2A-143%29%29%2F%282%2A1%29%29
-2%2B%28%28sqrt%284%2B572%29%29%2F2%29 -2-%28%28sqrt%284%2B572%29%29%2F2%29
-2%2B%28%28sqrt%28576%29%29%2F2%29 -2-%28%28sqrt%28576%29%29%2F2%29
-2%2B%2824%2F2%29 -2-%2824%2F2%29
-2%2B%2812%29 -2-%2812%29
x=highlight%2810%29, highlight%28-14%29