SOLUTION: {{{ 3x^2+5x-1=0 }}} Please help me solve this equation by completing the square

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: {{{ 3x^2+5x-1=0 }}} Please help me solve this equation by completing the square       Log On


   

Question 134329This question is from textbook beginning algebra
: +3x%5E2%2B5x-1=0+
Please help me solve this equation by completing the square This question is from textbook beginning algebra

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

3+x%5E2%2B5+x-1=0 Start with the given equation


3+x%5E2%2B5+x=1 Add 1 to both sides


3%28x%5E2%2B%285%2F3%29x%29=1 Factor out the leading coefficient 3


Take half of the x coefficient 5%2F3 to get 5%2F6 (ie %281%2F2%29%285%2F3%29=5%2F6).

Now square 5%2F6 to get 25%2F36 (ie %285%2F6%29%5E2=%285%2F6%29%285%2F6%29=25%2F36)




3%28x%5E2%2B%285%2F3%29x%2B25%2F36-25%2F36%29=1 Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of 25%2F36 does not change the equation



3%28%28x%2B5%2F6%29%5E2-25%2F36%29=1 Now factor x%5E2%2B%285%2F3%29x%2B25%2F36 to get %28x%2B5%2F6%29%5E2


3%28x%2B5%2F6%29%5E2-3%2825%2F36%29=1 Distribute


3%28x%2B5%2F6%29%5E2-25%2F12=1 Multiply


3%28x%2B5%2F6%29%5E2-25%2F12-1=1 Now add %2B1 to both sides to isolate y


3%28x%2B5%2F6%29%5E2-37%2F12=1 Combine like terms



3%28x%2B5%2F6%29%5E2=%2B37%2F12 Add 37%2F12 to both sides


%28x%2B5%2F6%29%5E2=%2837%2F12%29%2F%283%29 Divide both sides by 3


%28x%2B5%2F6%29%5E2=37%2F36 Reduce


Take the square root of both sides


Simplify


Subtract 5%2F6 from both sides


Combine the fractions



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Answer:


So our solutions are


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