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)   (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 (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

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 - .

The solution is

Here's your graph:
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