SOLUTION: give exact and approximate solutions to three decimal places x^2+5x-3=0

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Question 221511: give exact and approximate solutions to three decimal places

x^2+5x-3=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B5x-3=0 Start with the given equation.


Notice that the quadratic x%5E2%2B5x-3 is in the form of Ax%5E2%2BBx%2BC where A=1, B=5, and C=-3


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%28-3%29+%29%29%2F%282%281%29%29 Plug in A=1, B=5, and C=-3


x+=+%28-5+%2B-+sqrt%28+25-4%281%29%28-3%29+%29%29%2F%282%281%29%29 Square 5 to get 25.


x+=+%28-5+%2B-+sqrt%28+25--12+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-3%29 to get -12


x+=+%28-5+%2B-+sqrt%28+25%2B12+%29%29%2F%282%281%29%29 Rewrite sqrt%2825--12%29 as sqrt%2825%2B12%29


x+=+%28-5+%2B-+sqrt%28+37+%29%29%2F%282%281%29%29 Add 25 to 12 to get 37


x+=+%28-5+%2B-+sqrt%28+37+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-5%2Bsqrt%2837%29%29%2F%282%29 or x+=+%28-5-sqrt%2837%29%29%2F%282%29 Break up the expression.


So the solutions are x+=+%28-5%2Bsqrt%2837%29%29%2F%282%29 or x+=+%28-5-sqrt%2837%29%29%2F%282%29


which approximate to x=0.541 or x=-5.541