SOLUTION: Solve the equation using the quadratic formula. 4x^2 - 23x - 6 = 0

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Question 248215: Solve the equation using the quadratic formula.
4x^2 - 23x - 6 = 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 4%2Ax%5E2-23%2Ax-6=0 ( notice a=4, b=-23, and c=-6)





x+=+%28--23+%2B-+sqrt%28+%28-23%29%5E2-4%2A4%2A-6+%29%29%2F%282%2A4%29 Plug in a=4, b=-23, and c=-6




x+=+%2823+%2B-+sqrt%28+%28-23%29%5E2-4%2A4%2A-6+%29%29%2F%282%2A4%29 Negate -23 to get 23




x+=+%2823+%2B-+sqrt%28+529-4%2A4%2A-6+%29%29%2F%282%2A4%29 Square -23 to get 529 (note: remember when you square -23, you must square the negative as well. This is because %28-23%29%5E2=-23%2A-23=529.)




x+=+%2823+%2B-+sqrt%28+529%2B96+%29%29%2F%282%2A4%29 Multiply -4%2A-6%2A4 to get 96




x+=+%2823+%2B-+sqrt%28+625+%29%29%2F%282%2A4%29 Combine like terms in the radicand (everything under the square root)




x+=+%2823+%2B-+25%29%2F%282%2A4%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%2823+%2B-+25%29%2F8 Multiply 2 and 4 to get 8


So now the expression breaks down into two parts


x+=+%2823+%2B+25%29%2F8 or x+=+%2823+-+25%29%2F8


Lets look at the first part:


x=%2823+%2B+25%29%2F8


x=48%2F8 Add the terms in the numerator

x=6 Divide


So one answer is

x=6




Now lets look at the second part:


x=%2823+-+25%29%2F8


x=-2%2F8 Subtract the terms in the numerator

x=-1%2F4 Divide


So another answer is

x=-1%2F4


So our solutions are:

x=6 or x=-1%2F4