SOLUTION: Solve {{{sqrt(3x+4)-sqrt(2x+1)=1}}}

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Question 135510: Solve sqrt%283x%2B4%29-sqrt%282x%2B1%29=1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%283x%2B4%29-sqrt%282x%2B1%29=1 Start with the given equation


sqrt%283x%2B4%29=1%2Bsqrt%282x%2B1%29 Add sqrt%282x%2B1%29 to both sides


sqrt%283x%2B4%29=1%2Bsqrt%282x%2B1%29 Add sqrt%282x%2B1%29 to both sides


3x%2B4=%281%2Bsqrt%282x%2B1%29%29%5E2 Square both sides


3x%2B4=1%2B2%2Asqrt%282x%2B1%29%2B2x%2B1 Foil the right side


3x%2B4=2%2Asqrt%282x%2B1%29%2B2x%2B2 Combine like terms


3x%2B4-2x-2=2%2Asqrt%282x%2B1%29 Subtract 2x from both sides. Subtract 2 from both sides.

x%2B2=2%2Asqrt%282x%2B1%29 Combine like terms


%28x%2B2%29%5E2=4%2A%282x%2B1%29 Square both sides


x%5E2%2B4x%2B4=4%2A%282x%2B1%29 Foil the left side


x%5E2%2B4x%2B4=8x%2B4 Distribute


x%5E2%2B4x%2B4-8x-4=0 Subtract 8x from both sides. Subtract 4 from both sides.


x%5E2-4x=0 Combine like terms


x%28x-4%29=0 Factor the left side



Now set each factor equal to zero:
x=0 or x-4=0

x=0 or x=4 Now solve for x in each case


So our answers are

x=0 or x=4