Question

A number multiplied by 12 is equal to the sum of the square root of that same number and 36. What is that number?

Answer 1

Answer:

3.15

Step-by-step explanation:

Let the unknown number be n.

Then 12n = √n + 36

We must eliminate the √ operator.  One way to do this is to replace √n temporarily with x.  Then 12n = 12x^2, and we have 12x^2 - x - 36 = 0.  This is a quadratic with a= 12, b= -1 and c = -36

Solving for x using the quadratic formula:

       1 plus or minus √(1 - 4(12)(-36)

x = ----------------------------------------------

                        2(12)

      1 plus or minus √1729

x = -----------------------------------

                        24

       1 plus or minus 41.58

x = -----------------------------------

                    24

Since x = √n, n must be a positive number.  Thus,

       1 + 41.58

x = ---------------- = 1.77

            24

If x = 1.77 = √n, then n = 1.77^2 = 3.15.

Check:  Is this true?  A number multiplied by 12 is equal to the sum of the square root of that same number and 36.

12(3.15) = √3.15 + 36, or

 37.8    =  1.77 + 36  = 37.77     This checks out.

The number is 3.15