SOLUTION: x^2-2x-3=5

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Question 577538: x^2-2x-3=5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-2x-3=5 Start with the given equation.


x%5E2-2x-3-5=0 Subtract 5 from both sides.


x%5E2-2x-8=0 Combine like terms.


Notice that the quadratic x%5E2-2x-8 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-2, and C=-8


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-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%28-8%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-2, and C=-8


x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%28-8%29+%29%29%2F%282%281%29%29 Negate -2 to get 2.


x+=+%282+%2B-+sqrt%28+4-4%281%29%28-8%29+%29%29%2F%282%281%29%29 Square -2 to get 4.


x+=+%282+%2B-+sqrt%28+4--32+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-8%29 to get -32


x+=+%282+%2B-+sqrt%28+4%2B32+%29%29%2F%282%281%29%29 Rewrite sqrt%284--32%29 as sqrt%284%2B32%29


x+=+%282+%2B-+sqrt%28+36+%29%29%2F%282%281%29%29 Add 4 to 32 to get 36


x+=+%282+%2B-+sqrt%28+36+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%282+%2B-+6%29%2F%282%29 Take the square root of 36 to get 6.


x+=+%282+%2B+6%29%2F%282%29 or x+=+%282+-+6%29%2F%282%29 Break up the expression.


x+=+%288%29%2F%282%29 or x+=++%28-4%29%2F%282%29 Combine like terms.


x+=+4 or x+=+-2 Simplify.


So the solutions are x+=+4 or x+=+-2