SOLUTION: solve the following equation for x 7x^2-15X+5=3

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Question 104637: solve the following equation for x
7x^2-15X+5=3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
7x%5E2-15X%2B5=3 Start with the given equation


7x%5E2-15X%2B5-3=0 Subtract 3 from both sides


7x%5E2-15X%2B2=0 Combine like terms


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 7%2Ax%5E2-15%2Ax%2B2=0 ( notice a=7, b=-15, and c=2)





x+=+%28--15+%2B-+sqrt%28+%28-15%29%5E2-4%2A7%2A2+%29%29%2F%282%2A7%29 Plug in a=7, b=-15, and c=2




x+=+%2815+%2B-+sqrt%28+%28-15%29%5E2-4%2A7%2A2+%29%29%2F%282%2A7%29 Negate -15 to get 15




x+=+%2815+%2B-+sqrt%28+225-4%2A7%2A2+%29%29%2F%282%2A7%29 Square -15 to get 225 (note: remember when you square -15, you must square the negative as well. This is because %28-15%29%5E2=-15%2A-15=225.)




x+=+%2815+%2B-+sqrt%28+225%2B-56+%29%29%2F%282%2A7%29 Multiply -4%2A2%2A7 to get -56




x+=+%2815+%2B-+sqrt%28+169+%29%29%2F%282%2A7%29 Combine like terms in the radicand (everything under the square root)




x+=+%2815+%2B-+13%29%2F%282%2A7%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%2815+%2B-+13%29%2F14 Multiply 2 and 7 to get 14


So now the expression breaks down into two parts


x+=+%2815+%2B+13%29%2F14 or x+=+%2815+-+13%29%2F14


Lets look at the first part:


x=%2815+%2B+13%29%2F14


x=28%2F14 Add the terms in the numerator

x=2 Divide


So one answer is

x=2




Now lets look at the second part:


x=%2815+-+13%29%2F14


x=2%2F14 Subtract the terms in the numerator

x=1%2F7 Divide


So another answer is

x=1%2F7


So our solutions are:

x=2 or x=1%2F7