Question

Solve for x in the proportion 9/27x=x/x+3

Answer 1

Solve for x in the proportion 9/27x = x/x+3
I understand :
9/(27x) = x/(x + 3)
1/(3x) = x/(x + 3)
Cross multiply :
x + 3 = 3x^2
3x^2 - x - 3 = 0
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To find the roots for the quadratic equations :
Roots = (-b +/- sqrt(b^2 - 4ac)) / 2a
Where :
a = 3 b = -1 c = -3
Verification of the rationality :
sqrt(b^2 - 4ac)
sqrt((-1)^2 - (4*3*-3))
sqrt(1 + 36)
roots are rationals coz sqrt(b^2-4ac) = 6,083 ---> not negative

root 1 = (-b + 6,083) / 2a
root 1 = (1 + 6,083) / (2 *3)
root 1 = 7,083 / 6
root 1 --------------------> 1,181

root 2 = (-b - 6,083) / 2a
root 2 = (1 - 6,083) / (2 *3)
root 2 = -5,083 / 6
root 2 --------------------> -0,847
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So x ≈ 1.18 and x ≈ -0.85 (c)

Answer 2

set it equal to zero then use the quadratic formula

Answer 3

woah o.O okay so can you show me a simpler way of doing that. all of that was just alot o.O

Answer 4

lopez_hatesmath already tok over

Answer 5

yeahhh okay i gotchu

Answer 6

9/27x)=x/(x+3)
27^2-9x-27=0 divide by 9
3x^2-x-3=0
Using quadratic formula

Answer 7

3x^2-x-3=0 plug this in for the quadratic formula formula which is ( x=-b+ 0r -sqrt of b^2-4ac all over (2a)