SOLUTION: I have a test tomorrow and am having a lot of trouble with quadratic equations. i understand some things, but others do not make sense at all. below are 3 problems that i do not un

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Question 115722: I have a test tomorrow and am having a lot of trouble with quadratic equations. i understand some things, but others do not make sense at all. below are 3 problems that i do not understand how to solve. if you could solve the problem and show the steps, that would really help me a lot.
1. 2x^2 - 14x - 10 = 0 (must be solved by factoring or by completing the square, cannot use the quadratic formula)

Answer by jim_thompson5910(28550) About Me  (Show Source):
You can put this solution on YOUR website!

2x%5E2-14x-10=0 Start with the given equation


2x%5E2-14x=10 Add 10 to both sides
2%28x%5E2-7x%29=10 Factor out the leading coefficient 2. This step is important since we want the x%5E2 coefficient to be equal to 1.



Take half of the x coefficient -7 to -7%2F2
Now square -7%2F2 to get 49%2F4



2%28x%5E2-7x%2B49%2F4%29=10%2B%2849%2F4%29%282%29 Add this result (12.25) to the expression x%5E2-7x inside the parenthesis. Now the expression x%5E2-7x%2B49%2F4 is a perfect square trinomial. Now add the result %2849%2F4%29%282%29 (remember we factored out a 2) to the right side.



2%28x-7%2F2%29%5E2=10%2B%2849%2F4%29%282%29 Factor x%5E2-7x%2B49%2F4 into %28x-7%2F2%29%5E2


2%28x-7%2F2%29%5E2=10%2B49%2F2 Multiply 49%2F4 and 2 to get 49%2F2



2%28x-7%2F2%29%5E2=69%2F2 Combine like terms on the right side

%28x-7%2F2%29%5E2=69%2F4 Divide both sides by 2


x-7%2F2=0%2B-sqrt%2869%2F4%29 Take the square root of both sides


x-7%2F2=0%2B-sqrt%2869%29%2F2 Simplify

x=7%2F2%2B-sqrt%2869%29%2F2 Add 7%2F2 to both sides to isolate x.


x=%287%2B-sqrt%2869%29%29%2F2 Combine the fractions