SOLUTION: can you figure out the answer to this equation, 3x^2+14x+94 using the completing the square method?

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Question 241751: can you figure out the answer to this equation, 3x^2+14x+94 using the completing the square method?
Found 2 solutions by jim_thompson5910, JimboP1977:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x%5E2%2B14x%2B94 Start with the given expression.


3%28x%5E2%2B%2814%2F3%29x%2B94%2F3%29 Factor out the x%5E2 coefficient 3. This step is very important: the x%5E2 coefficient must be equal to 1.


Take half of the x coefficient 14%2F3 to get 7%2F3. In other words, %281%2F2%29%2814%2F3%29=7%2F3.


Now square 7%2F3 to get 49%2F9. In other words, %287%2F3%29%5E2=%287%2F3%29%287%2F3%29=49%2F9


3%28x%5E2%2B%2814%2F3%29x%2Bhighlight%2849%2F9-49%2F9%29%2B94%2F3%29 Now add and subtract 49%2F9 inside the parenthesis. Make sure to place this after the "x" term. Notice how 49%2F9-49%2F9=0. So the expression is not changed.


3%28%28x%5E2%2B%2814%2F3%29x%2B49%2F9%29-49%2F9%2B94%2F3%29 Group the first three terms.


3%28%28x%2B7%2F3%29%5E2-49%2F9%2B94%2F3%29 Factor x%5E2%2B%2814%2F3%29x%2B49%2F9 to get %28x%2B7%2F3%29%5E2.


3%28%28x%2B7%2F3%29%5E2%2B233%2F9%29 Combine like terms.


3%28x%2B7%2F3%29%5E2%2B3%28233%2F9%29 Distribute.


3%28x%2B7%2F3%29%5E2%2B233%2F3 Multiply.


So after completing the square, 3x%5E2%2B14x%2B94 transforms to 3%28x%2B7%2F3%29%5E2%2B233%2F3. So 3x%5E2%2B14x%2B94=3%28x%2B7%2F3%29%5E2%2B233%2F3.


So 3x%5E2%2B14x%2B94=0 is equivalent to 3%28x%2B7%2F3%29%5E2%2B233%2F3=0.


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So to solve 3x%5E2%2B14x%2B94=0, we can solve 3%28x%2B7%2F3%29%5E2%2B233%2F3=0


3%28x%2B7%2F3%29%5E2%2B233%2F3=0 Start with the given equation.


3%28x%2B7%2F3%29%5E2=0-233%2F3Subtract 233%2F3 from both sides.


3%28x%2B7%2F3%29%5E2=-233%2F3 Combine like terms.


%28x%2B7%2F3%29%5E2=%28-233%2F3%29%2F%283%29 Divide both sides by 3.


%28x%2B7%2F3%29%5E2=-233%2F9 Reduce.


x%2B7%2F3=%22%22%2B-sqrt%28-233%2F9%29 Take the square root of both sides.


x%2B7%2F3=sqrt%28-233%2F9%29 or x%2B7%2F3=-sqrt%28-233%2F9%29 Break up the "plus/minus" to form two equations.


x%2B7%2F3=%28i%2Asqrt%28233%29%29%2F3 or x%2B7%2F3=-%28i%2Asqrt%28233%29%29%2F3 Simplify the square root.


x=-7%2F3%2B%28i%2Asqrt%28233%29%29%2F3 or x=-7%2F3-%28i%2Asqrt%28233%29%29%2F3 Subtract 7%2F3 from both sides.


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Answer:


So the solutions are x=-7%2F3%2B%28i%2Asqrt%28233%29%29%2F3 or x=-7%2F3-%28i%2Asqrt%28233%29%29%2F3.


Answer by JimboP1977(311) About Me  (Show Source):
You can put this solution on YOUR website!
No real solutions to this equation as does not cross the x-axis.