Before solving the equation, we'll impose conditions of
existence of the square root.
7x+14 >=
0
Wer'll subtract 14 both
sides:
7x >= -14
We'll
divide by 7: x >= -2
The interval of admissible
solutions for the given equation is:
[-2 ,
+infinite)
Now, we'll solve the
equation:
sqrt 7x+14 = x
We'll
square raise both sides:
7x + 14 =
x^2
We'll move all terms to one side and we'll use the
symmetrical property:
x^2 - 7x - 14 =
0
We'll apply the quadratic
formula:
x1 =
[7+sqrt(49+56)]/2
x2
= [7-sqrt(49+56)]/2
since sqrt 105 = 10.24
approx
x1 =
(7+10.24)/2
x1 = 8.62
approx.
x2 =
(7-10.24)/2
x2 = -1.62
approx.
Since both values belong to the
interval of admissible values, they are accepted as solutions of the given
equation.
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