SOLUTION: Solve for x when 2x squared + 5x=12

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Question 506795: Solve for x when 2x squared + 5x=12
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x%5E2%2B5x=12 Start with the given equation.


2x%5E2%2B5x-12=0 Get every term to the left side.


Notice that the quadratic 2x%5E2%2B5x-12 is in the form of Ax%5E2%2BBx%2BC where A=2, B=5, and C=-12


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%285%29+%2B-+sqrt%28+%285%29%5E2-4%282%29%28-12%29+%29%29%2F%282%282%29%29 Plug in A=2, B=5, and C=-12


x+=+%28-5+%2B-+sqrt%28+25-4%282%29%28-12%29+%29%29%2F%282%282%29%29 Square 5 to get 25.


x+=+%28-5+%2B-+sqrt%28+25--96+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-12%29 to get -96


x+=+%28-5+%2B-+sqrt%28+25%2B96+%29%29%2F%282%282%29%29 Rewrite sqrt%2825--96%29 as sqrt%2825%2B96%29


x+=+%28-5+%2B-+sqrt%28+121+%29%29%2F%282%282%29%29 Add 25 to 96 to get 121


x+=+%28-5+%2B-+sqrt%28+121+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%28-5+%2B-+11%29%2F%284%29 Take the square root of 121 to get 11.


x+=+%28-5+%2B+11%29%2F%284%29 or x+=+%28-5+-+11%29%2F%284%29 Break up the expression.


x+=+%286%29%2F%284%29 or x+=++%28-16%29%2F%284%29 Combine like terms.


x+=+3%2F2 or x+=+-4 Simplify.


So the solutions are x+=+3%2F2 or x+=+-4

Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
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Thanks,

Jim