SOLUTION: Find the real solutions of √ x 2 + 144 = x + 6

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Question 921154: Find the real solutions of √ x 2 + 144 = x + 6
Answer by srinivas.g(540) About Me  (Show Source):
You can put this solution on YOUR website!
sqtrt(X) +144 =x+6
substrat 144 on both sides
sqrt(x) +144-6 =x+6-6
sqrt(x) +138=x
sqrt(x)=x-138
squaring on both sides
sqrt(x)*sqrt(x) = (x-138)*(x-138)
x = x(x-138)-138(x-138)
x = x^2 -138*x-138*x -138*(-138)
x = x^2 -138x-138x+19044
x =x^2 -276x+19044
subtract x on both sides
x-x =x^2 -276x+19044-x
0=x^2-275x+19044
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-275x%2B19044+=+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=%28-275%29%5E2-4%2A1%2A19044=-551.

The discriminant -551 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -551 is + or - sqrt%28+551%29+=+23.473389188611.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-275%2Ax%2B19044+%29