SOLUTION: Solve the equation by extracting square roots - list both the exact solution and the decimal solution rounded to two decimal places. (x+13)^2 = 25

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Question 119461This question is from textbook Trigonometry
: Solve the equation by extracting square roots - list both the exact solution and the decimal solution rounded to two decimal places.
(x+13)^2 = 25 This question is from textbook Trigonometry

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given equation



Take the square root of both sides




Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



Subtract 13 from both sides to isolate x.


Break down the expression into two parts: 




   or


Now combine like terms for each expression: 

   or



-----------------------------------
Answer:
So our solution is 

  or


Notice when we graph the equations y=%28x%2B13%29%5E2 and y=25 we get:

graph of y=%28x%2B13%29%5E2 (red) and y=25 (green)



Here we can see that the two equations intersect at x values of x=-8 and x=-18, so this verifies our answer.