Answer: x = 64[/tex]
Step-by-step explanation:
In mathematical notation, the problem is to solve the following equation
[tex]\sqrt{x} + x = 72[/tex]
We can assume that the new variable is [tex](x^{1/2})[/tex], so the equation is:
[tex](x^{1/2} )^{2} + (x^{1/2} ) -72 = 0[/tex]
We can solve this like a normal quadratic equation
[tex]x^{1/2} = \frac{-1±\sqrt{1-4(1)(-72)}}{2}[/tex]
[tex]x^{1/2} = \frac{-1±17}{2}[/tex],
The solutions are
[tex]x^{1/2} = -9 \\ x^{1/2} = 8[/tex]
We use the positive one, because a square can not be negative
So, [tex]x^{1/2} = 8, x = 64[/tex]
To prove the answer
[tex]\sqrt{64} + 64 = 72[/tex]
