SOLUTION: Use the quadratic formula to solve each of the following quadratic equations. 2x2 - 5x = 3

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Question 115427: Use the quadratic formula to solve each of the following quadratic equations.
2x2 - 5x = 3
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Start with the given equation


Move all of the terms to the left side


Now let's use the quadratic formula to solve for x:


Starting with the general quadratic



the general solution using the quadratic equation is:





So lets solve ( notice , , and )




Plug in a=2, b=-5, and c=-3



Negate -5 to get 5



Square -5 to get 25 (note: remember when you square -5, you must square the negative as well. This is because .)



Multiply to get



Combine like terms in the radicand (everything under the square root)



Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



Multiply 2 and 2 to get 4

So now the expression breaks down into two parts

or

Lets look at the first part:



Add the terms in the numerator
Divide

So one answer is




Now lets look at the second part:



Subtract the terms in the numerator
Divide

So another answer is


So our solutions are:
or

Notice when we graph , we get:



and we can see that the roots are and . This verifies our answer
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