SOLUTION: solve and find the value for x which satisfies the equation 2x^2-4=7x

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Question 395305: solve and find the value for x which satisfies the equation
2x^2-4=7x

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x%5E2-4=7x Start with the given equation.


2x%5E2-4-7x=0 Subtract 7x from both sides.


2x%5E2-7x-4=0 Rearrange the terms.


Notice that the quadratic 2x%5E2-7x-4 is in the form of Ax%5E2%2BBx%2BC where A=2, B=-7, and C=-4


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-%28-7%29+%2B-+sqrt%28+%28-7%29%5E2-4%282%29%28-4%29+%29%29%2F%282%282%29%29 Plug in A=2, B=-7, and C=-4


x+=+%287+%2B-+sqrt%28+%28-7%29%5E2-4%282%29%28-4%29+%29%29%2F%282%282%29%29 Negate -7 to get 7.


x+=+%287+%2B-+sqrt%28+49-4%282%29%28-4%29+%29%29%2F%282%282%29%29 Square -7 to get 49.


x+=+%287+%2B-+sqrt%28+49--32+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-4%29 to get -32


x+=+%287+%2B-+sqrt%28+49%2B32+%29%29%2F%282%282%29%29 Rewrite sqrt%2849--32%29 as sqrt%2849%2B32%29


x+=+%287+%2B-+sqrt%28+81+%29%29%2F%282%282%29%29 Add 49 to 32 to get 81


x+=+%287+%2B-+sqrt%28+81+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%287+%2B-+9%29%2F%284%29 Take the square root of 81 to get 9.


x+=+%287+%2B+9%29%2F%284%29 or x+=+%287+-+9%29%2F%284%29 Break up the expression.


x+=+%2816%29%2F%284%29 or x+=++%28-2%29%2F%284%29 Combine like terms.


x+=+4 or x+=+-1%2F2 Simplify.


So the solutions are x+=+4 or x+=+-1%2F2

If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim