You are correct there's at least one obtuse angle
Here I copy the steps and indicate where the error is.
Square root of negative 2x plus 1 − 3 = x=> <span>this is the starting equation
</span>
√[ - 2x + 1] - 3 = x
Square root of negative 2x plus 1 − 3 + 3 = x + 3 in this step she added 3 to each side, which is fine
<span> Square root
of negative 2x plus 1 = x + 3 <span>she made the addtions => fine</span></span>
Square root of negative 2x plus 1 − 1 = x + 3 – 1 due to <span>plus 1 in inside the square root, this step will not help</span>
<span> Square root
of negative 2 x = x + 2 <span>wrong! she cannot simplify - 1 that is out of the square root with +1 that is inside the square root
</span></span>
<span>Then, from here on all is wrong, but she made other additional mistakes.</span>
(Square root of negative 2 x)2 = (x − 4)2 −2x <span> the right side should be (x+2)^2 which is x^2 + 4x +4 not (x-4)^2 - 2x</span>
Later she made a mistake changing the sign of -8x to +8x
Those are the mistakes. Finally, the global error is that she should verify whether the found values satisfied the original equation.
Answer:
Shortest distance from the mountain is 3.17 miles.
Step-by-step explanation:
From the figure attached,
Let a mountain is located at point A.
Angle between the mountain and point B (∠B) = 53°
Angle between the mountain and point C (∠C) = 78°
Distance between these points = 3 miles
Since, m∠A + m∠B + m∠C = 180°
m∠A + 53° + 78° = 180°
m∠A = 180°- 131° = 49°
By applying sine rule in triangle ABC,
AC = 
AC = 3.17 miles
AB = 
AB = 3.89 miles
Therefore, shortest distance from the mountain is 3.17 miles.
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