SOLUTION: (4x+3)^2=4

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Question 1103691: (4x+3)^2=4
Found 2 solutions by stanbon, ikleyn:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(4x+3)^2=4
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Take the square root of both sides
4x+3 = 2 or 4x+3 = -2
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4x = -1 or 4x = -5
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x = -1/4 or x = -5/4
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Cheers,
Stan H.
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Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Take square root from both sides.


Then your original equation deploys in TWO independent equations:


1)  4x + 3 = 2   ====>  4x = 2 - 3 = -1   ====>  x = %28-1%29%2F4 = -1%2F4 = -0.25.


2)  4x + 3 = -2  ====>  4x = -2 - 3 = -5  ====>  x = %28-5%29%2F4 = -5%2F4 = -1.25.


Answer. Two solutions are  x= -0.25  and  x= -1.25.


There are many ways (more than one way) to reduce the original equations to linear equations 1) and 2).

All these ways lead to the same set of solutions.



Visually, this plot might be helpful:




Plot y = %284x%2B3%29%5E2 (red) and y = 4 (green)