SOLUTION: use quad formula to solve 5x^2-7x-3=0

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Question 884370: use quad formula to solve 5x^2-7x-3=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

5x%5E2-7x-3=0 Start with the given equation.


Notice that the quadratic 5x%5E2-7x-3 is in the form of Ax%5E2%2BBx%2BC where A=5, B=-7, 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-%28-7%29+%2B-+sqrt%28+%28-7%29%5E2-4%285%29%28-3%29+%29%29%2F%282%285%29%29 Plug in A=5, B=-7, and C=-3


x+=+%287+%2B-+sqrt%28+%28-7%29%5E2-4%285%29%28-3%29+%29%29%2F%282%285%29%29 Negate -7 to get 7.


x+=+%287+%2B-+sqrt%28+49-4%285%29%28-3%29+%29%29%2F%282%285%29%29 Square -7 to get 49.


x+=+%287+%2B-+sqrt%28+49--60+%29%29%2F%282%285%29%29 Multiply 4%285%29%28-3%29 to get -60


x+=+%287+%2B-+sqrt%28+49%2B60+%29%29%2F%282%285%29%29 Rewrite sqrt%2849--60%29 as sqrt%2849%2B60%29


x+=+%287+%2B-+sqrt%28+109+%29%29%2F%282%285%29%29 Add 49 to 60 to get 109


x+=+%287+%2B-+sqrt%28+109+%29%29%2F%2810%29 Multiply 2 and 5 to get 10.


x+=+%287%2Bsqrt%28109%29%29%2F%2810%29 or x+=+%287-sqrt%28109%29%29%2F%2810%29 Break up the expression.


So the exact solutions are x+=+%287%2Bsqrt%28109%29%29%2F%2810%29 or x+=+%287-sqrt%28109%29%29%2F%2810%29


Use a calculator to get these approximate solutions (note: you evaluate the exact solutions to get the approximate solutions)


x+=+1.74403065089106 or x+=+-0.34403065089106