SOLUTION: Solve for all real roots (x-4)^2=36

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Question 235302: Solve for all real roots
(x-4)^2=36
Found 2 solutions by jim_thompson5910, MathPro:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28x-4%29%5E2=36 Start with the given equation.


x-4=%22%22%2B-sqrt%2836%29 Take the square root of both sides.


x-4=sqrt%2836%29 or x-4=-sqrt%2836%29 Break up the "plus/minus" to form two equations.


x-4=6 or x-4=-6 Take the square root of 36 to get 6.


x=4%2B6 or x=4-6 Add 4 to both sides.


x=10 or x=-2 Combine like terms.


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Answer:


So the solutions are x=10 or x=-2.

Answer by MathPro(14) About Me  (Show Source):
You can put this solution on YOUR website!
Good evening,
Your problem is: Solve for all real roots (x-4)^2=36
The first term is squared so let’s try to get rid of that by taking the square root of both sides of the equation:
(x-4)^[2(1/2)] = 36^1/2
x - 4 = 6
Let’s solve for x by adding 4 to both sides:
x – 4 + 4 = 6 + 4
x =10
Check the answer by substituting for x in the original equation:
(10-4)^2 = 36
36 = 36
The left-hand-side is equal to the right-hand-side, so the answer is correct.
Good Luck!
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