SOLUTION: Can someone help me? #31. Solve each equation and check for extraneous solutions. 2√w+4=5 thank you

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Question 157304This question is from textbook elementary and intermediate algebra
: Can someone help me? #31. Solve each equation and check for extraneous solutions. 2√w+4=5
thank you This question is from textbook elementary and intermediate algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2%2Asqrt%28w%2B4%29=5 Start with the given equation


4%28w%2B4%29=25 Square both sides


4w%2B16=25 Distribute.


4w=25-16 Subtract 16 from both sides.


4w=9 Combine like terms on the right side.


w=%289%29%2F%284%29 Divide both sides by 4 to isolate w.


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Answer:

So the answer is w=9%2F4 which in decimal form is w=2.25.



Check:

2%2Asqrt%28w%2B4%29=5 Start with the given equation


2%2Asqrt%289%2F4%2B4%29=5 Plug in w=9%2F4


2%2Asqrt%2825%2F4%29=5 Add


2%2A%285%2F2%29=5 Take the square root


10%2F2=5 Multiply


5=5 Reduce. Since the equation is true, this verifies our answer.