SOLUTION: solve for x 4x(x-9)-5x(x-8)=-5

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Question 266442: solve for x 4x(x-9)-5x(x-8)=-5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
4x%28x-9%29-5x%28x-8%29=-5 Start with the given equation.


4x%5E2-36x-5x%5E2%2B40x%2B5=0 Add 5 to both sides.


-x%5E2%2B4x%2B5=0 Combine like terms.


Notice that the quadratic -x%5E2%2B4x%2B5 is in the form of Ax%5E2%2BBx%2BC where A=-1, B=4, and C=5


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-%284%29+%2B-+sqrt%28+%284%29%5E2-4%28-1%29%285%29+%29%29%2F%282%28-1%29%29 Plug in A=-1, B=4, and C=5


x+=+%28-4+%2B-+sqrt%28+16-4%28-1%29%285%29+%29%29%2F%282%28-1%29%29 Square 4 to get 16.


x+=+%28-4+%2B-+sqrt%28+16--20+%29%29%2F%282%28-1%29%29 Multiply 4%28-1%29%285%29 to get -20


x+=+%28-4+%2B-+sqrt%28+16%2B20+%29%29%2F%282%28-1%29%29 Rewrite sqrt%2816--20%29 as sqrt%2816%2B20%29


x+=+%28-4+%2B-+sqrt%28+36+%29%29%2F%282%28-1%29%29 Add 16 to 20 to get 36


x+=+%28-4+%2B-+sqrt%28+36+%29%29%2F%28-2%29 Multiply 2 and -1 to get -2.


x+=+%28-4+%2B-+6%29%2F%28-2%29 Take the square root of 36 to get 6.


x+=+%28-4+%2B+6%29%2F%28-2%29 or x+=+%28-4+-+6%29%2F%28-2%29 Break up the expression.


x+=+%282%29%2F%28-2%29 or x+=++%28-10%29%2F%28-2%29 Combine like terms.


x+=+-1 or x+=+5 Reduce.


So the solutions are x+=+-1 or x+=+5