SOLUTION: I need help on writing equations using symbols.. Here it is : When you square five times a number you get three more than the number.

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Question 859286: I need help on writing equations using symbols..
Here it is : When you square five times a number you get three more than the number.
Found 2 solutions by ewatrrr, rothauserc:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

Question States**

(5x)^2 = x + 3

 25x^2 - x - 3 = 0




 
Solved by pluggable solver: SOLVE quadratic equation with variable


Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 25x%5E2%2B-1x%2B-3+=+0) has the following solutons:

  

  x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

  

  For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

  

  First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-1%29%5E2-4%2A25%2A-3=301.

  

  Discriminant d=301 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+301+%29%29%2F2%5Ca.

  

    x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+301+%29%29%2F2%5C25+=+0.366987031457949

    x%5B2%5D+=+%28-%28-1%29-sqrt%28+301+%29%29%2F2%5C25+=+-0.326987031457949

    

    Quadratic expression 25x%5E2%2B-1x%2B-3 can be factored:

  25x%5E2%2B-1x%2B-3+=+25%28x-0.366987031457949%29%2A%28x--0.326987031457949%29

  Again, the answer is: 0.366987031457949, -0.326987031457949.
Here's your graph:

graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+25%2Ax%5E2%2B-1%2Ax%2B-3+%29

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
let x be the number
(5x)^2 = x + 3
this can be solved for x using the quadratic formula if you need to