SOLUTION: What is the solution set of the equation x^2+2x-15=0? thanks for your help.

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Question 602526: What is the solution set of the equation x^2+2x-15=0?

thanks for your help.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B2x-15=0 Start with the given equation.


Notice that the quadratic x%5E2%2B2x-15 is in the form of Ax%5E2%2BBx%2BC where A=1, B=2, and C=-15


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-%282%29+%2B-+sqrt%28+%282%29%5E2-4%281%29%28-15%29+%29%29%2F%282%281%29%29 Plug in A=1, B=2, and C=-15


x+=+%28-2+%2B-+sqrt%28+4-4%281%29%28-15%29+%29%29%2F%282%281%29%29 Square 2 to get 4.


x+=+%28-2+%2B-+sqrt%28+4--60+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-15%29 to get -60


x+=+%28-2+%2B-+sqrt%28+4%2B60+%29%29%2F%282%281%29%29 Rewrite sqrt%284--60%29 as sqrt%284%2B60%29


x+=+%28-2+%2B-+sqrt%28+64+%29%29%2F%282%281%29%29 Add 4 to 60 to get 64


x+=+%28-2+%2B-+sqrt%28+64+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-2+%2B-+8%29%2F%282%29 Take the square root of 64 to get 8.


x+=+%28-2+%2B+8%29%2F%282%29 or x+=+%28-2+-+8%29%2F%282%29 Break up the expression.


x+=+%286%29%2F%282%29 or x+=++%28-10%29%2F%282%29 Combine like terms.


x+=+3 or x+=+-5 Simplify.


So the solutions are x+=+3 or x+=+-5

This means that the solution set is {3,-5}

Note: order of the solutions doesn't matter as you can also write the solution set as {-5,3}