SOLUTION: The exact x values of x^2+4x-20=0

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Question 631077: The exact x values of x^2+4x-20=0
Answer by jim_thompson5910(28715) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B4x-20=0 Start with the given equation.


Notice that the quadratic x%5E2%2B4x-20 is in the form of Ax%5E2%2BBx%2BC where A=1, B=4, and C=-20


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%281%29%28-20%29+%29%29%2F%282%281%29%29 Plug in A=1, B=4, and C=-20


x+=+%28-4+%2B-+sqrt%28+16-4%281%29%28-20%29+%29%29%2F%282%281%29%29 Square 4 to get 16.


x+=+%28-4+%2B-+sqrt%28+16--80+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-20%29 to get -80


x+=+%28-4+%2B-+sqrt%28+16%2B80+%29%29%2F%282%281%29%29 Rewrite sqrt%2816--80%29 as sqrt%2816%2B80%29


x+=+%28-4+%2B-+sqrt%28+96+%29%29%2F%282%281%29%29 Add 16 to 80 to get 96


x+=+%28-4+%2B-+sqrt%28+96+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-4+%2B-+4%2Asqrt%286%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-4%29%2F%282%29+%2B-+%284%2Asqrt%286%29%29%2F%282%29 Break up the fraction.


x+=+-2+%2B-+2%2Asqrt%286%29 Reduce.


x+=+-2%2B2%2Asqrt%286%29 or x+=+-2-2%2Asqrt%286%29 Break up the expression.


So the solutions are x+=+-2%2B2%2Asqrt%286%29 or x+=+-2-2%2Asqrt%286%29

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