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This problem is ultra tough. If anyone could help me on this one it would be very much appreciated.

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2 Answers

sqrt(2w+5) +4 = sqrt(25)
 
Now sqrt(25) = +5 and -5
 
1. Substituting sqrt(25) = +5 in the above eqn
 
sqrt(2w+5) +4 = 5 
sqrt(2w+5) = 1
2w+5 = 1   ( By squaring both sides)
w = -2
 
2. Substituting sqrt(25) = -5 in the main eqn
sqrt(2w+5) +4 = -5
sqrt(2w+5) = -9
2w+5 = 81  (By squaring both sides)
w = 38
 
So 2 possible solutions are w=-2 and w=38

Comments

√25=5, the principal root or the nonnegative root, so -5 cannot be used.
First step is to square root the 25, which is 5. Then subtract the 4 from both sides to get √(2w+5) = 1. You then have to get rid of the square root by squaring both sides, this would lead to 2w + 5 = 1. You then subtracdt 5 from both sides to get 2w = -4 and then divide by 2 to get w = -2. 
 
You can plug any answer you get back into the equation to see if you're right. So let's do that:
 
√(2(-2)+5) + 4 = 5
√(-4 + 5) + 4 = 5
√(1) + 4 = 5
1 + 4 = 5
5 = 5 *this is equal on both sides, therefore the correct answer!*