SOLUTION: The sum of a number and three times its square is 200. Find the number.

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Question 783548: The sum of a number and three times its square is 200. Find the number.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
The sum of a number x and three times its square 3x%5E2 is 200.
so,
x%2B3x%5E2=200
+3x%5E2%2Bx-200=+0....use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A3%2A%28-200%29+%29%29%2F%282%2A3%29+
x+=+%28-1+%2B-+sqrt%28+1+%2B2400%29+%29%29%2F6+
x+=+%28-1+%2B-+sqrt%282401%29+%29%29%2F6+
x+=+%28-1+%2B-+49+%29%29%2F6+
solutions:
x+=+%28-1+%2B+49+%29%29%2F6+
x+=+48%2F6+
x+=+8+
or
x+=+%28-1-+49+%29%29%2F6+
x+=+-50%2F6+
x+=-8.33+
check:
x%2B3x%5E2=200
8%2B3%2A8%5E2=200
8%2B3%2A64=200
8%2B182=200
200=200

-8.33%2B3%2A-8.33%5E2=200
-8.33+%2B3%2A8%5E2=200
-8.33+%2B3%2A69.4+=200
-8.33+%2B208.2=200
199.9=200
200=200