SOLUTION: x(x+5)=14

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Question 336187: x(x+5)=14
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%28x%2B5%29=14 Start with the given equation.


x%5E2%2B5x=14 Distribute


x%5E2%2B5x-14=0 Subtract 14 from both sides.


Notice that the quadratic x%5E2%2B5x-14 is in the form of Ax%5E2%2BBx%2BC where A=1, B=5, and C=-14


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%281%29%28-14%29+%29%29%2F%282%281%29%29 Plug in A=1, B=5, and C=-14


x+=+%28-5+%2B-+sqrt%28+25-4%281%29%28-14%29+%29%29%2F%282%281%29%29 Square 5 to get 25.


x+=+%28-5+%2B-+sqrt%28+25--56+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-14%29 to get -56


x+=+%28-5+%2B-+sqrt%28+25%2B56+%29%29%2F%282%281%29%29 Rewrite sqrt%2825--56%29 as sqrt%2825%2B56%29


x+=+%28-5+%2B-+sqrt%28+81+%29%29%2F%282%281%29%29 Add 25 to 56 to get 81


x+=+%28-5+%2B-+sqrt%28+81+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-5+%2B-+9%29%2F%282%29 Take the square root of 81 to get 9.


x+=+%28-5+%2B+9%29%2F%282%29 or x+=+%28-5+-+9%29%2F%282%29 Break up the expression.


x+=+%284%29%2F%282%29 or x+=++%28-14%29%2F%282%29 Combine like terms.


x+=+2 or x+=+-7 Simplify.


So the solutions are x+=+2 or x+=+-7


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

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Jim