SOLUTION: A number increased by its square is equal to 9 times the next number. Find the number

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Question 930177: A number increased by its square is equal to 9 times the next number. Find the number
Found 2 solutions by ptfile, MathTherapy:
Answer by ptfile(81) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = smaller number
x+1= larger number
A number increased by its square is equal to 9 times the next number
x^2 = 9(x+1)
x^2 = 9x+9
x^2-9x-9 = 0
Use Quadratic formula to solve for x
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%289+%2B-+sqrt%28+81%2B36+%29%29%2F%282%29+
x+=+%289+%2B-+sqrt%28+117+%29%29%2F%282%29+
x=9.9083269131959839396788319012057 or 10
or
x=-0.908326913195983939678831901205 or -1
Substitute x with 10
(10)^2 = 9(10+1)
100 = 9(11)
100 = 99
Substitute x with -1
(-1)^2 = 9(-1+1)
1 = 9(0)
1 = 0
The number is -1 or 10.
You could also use completing the square to solve for x
x^2-9x-9= 0
Add 9 on both side
x^2-9x+9= 0+9
x^2-9x = 9
Divide B coefficient by 2 and square it. Then add it on both side
x^2-9x+81/4=9+81/4
x^2-9x+81/4=36/4+81/4
x^2-9x+81/4=117/4
(x-9/2)^2=117/4
Square root on both side
√(x-9/2)^2 = √117/4
x-9/2 = 3/2√13
Add 9/2 on both side. Add ± on the right side.
x-9/2+9/2 =9/2±3/2√13
x = 9/2 ±3/2√13

x = 9.9083269131959839396788319012057 or 10
or
x = -0.908326913195983939678831901205 or -1

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
A number increased by its square is equal to 9 times the next number. Find the number 
Number can either be highlight_green%289%29, or highlight_green%28-+1%29

You can do the check!! 

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