SOLUTION: Find the x-values of the intersections from the graphs of {{{y=4x^2-4x+2}}} and {{{6x+y=4}}}

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Question 140630: Find the x-values of the intersections from the graphs of y=4x%5E2-4x%2B2 and 6x%2By=4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
6x%2By=4 Start with the second equation


y=4-6x Subtract 6x from both sides


y=4x%5E2-4x%2B2 Move onto the first equation


4-6x=4x%5E2-4x%2B2 Plug in y=4-6x


0=4x%5E2-4x%2B2-4%2B6x Subtract 4 from both sides. Add 6x to both sides.


0=4x%5E2%2B2x-2 Combine like terms


2%28x%2B1%29%282x-1%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
x%2B1=0 or 2x-1=0

x=-1 or x=1%2F2 Now solve for x in each case




So the x-values of the intersections are

x=-1 or x=1%2F2