SOLUTION: Use the quadratic formula to solve the equation. 3x^2 - 4x - 7 = 0

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Question 102395: Use the quadratic formula to solve the equation.
3x^2 - 4x - 7 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 3%2Ax%5E2-4%2Ax-7=0 ( notice a=3, b=-4, and c=-7)





x+=+%28--4+%2B-+sqrt%28+%28-4%29%5E2-4%2A3%2A-7+%29%29%2F%282%2A3%29 Plug in a=3, b=-4, and c=-7




x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%2A3%2A-7+%29%29%2F%282%2A3%29 Negate -4 to get 4




x+=+%284+%2B-+sqrt%28+16-4%2A3%2A-7+%29%29%2F%282%2A3%29 Square -4 to get 16 (note: remember when you square -4, you must square the negative as well. This is because %28-4%29%5E2=-4%2A-4=16.)




x+=+%284+%2B-+sqrt%28+16%2B84+%29%29%2F%282%2A3%29 Multiply -4%2A-7%2A3 to get 84




x+=+%284+%2B-+sqrt%28+100+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)




x+=+%284+%2B-+10%29%2F%282%2A3%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%284+%2B-+10%29%2F6 Multiply 2 and 3 to get 6


So now the expression breaks down into two parts


x+=+%284+%2B+10%29%2F6 or x+=+%284+-+10%29%2F6


Lets look at the first part:


x=%284+%2B+10%29%2F6


x=14%2F6 Add the terms in the numerator

x=7%2F3 Divide


So one answer is

x=7%2F3




Now lets look at the second part:


x=%284+-+10%29%2F6


x=-6%2F6 Subtract the terms in the numerator

x=-1 Divide


So another answer is

x=-1


So our solutions are:

x=7%2F3 or x=-1