SOLUTION: Give exact and approximate solutions to three decimal places. x^2-5x+5=0. Find the x-intercepts. What are the solutions? What are the x-intercepts? Thank you!

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Give exact and approximate solutions to three decimal places. x^2-5x+5=0. Find the x-intercepts. What are the solutions? What are the x-intercepts? Thank you!      Log On


   

Question 221453: Give exact and approximate solutions to three decimal places. x^2-5x+5=0. Find the x-intercepts.
What are the solutions?
What are the x-intercepts?
Thank you!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-5x%2B5=0 Start with the given equation.


Notice that the quadratic x%5E2-5x%2B5 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-5, and C=5


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-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%281%29%285%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-5, and C=5


x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%281%29%285%29+%29%29%2F%282%281%29%29 Negate -5 to get 5.


x+=+%285+%2B-+sqrt%28+25-4%281%29%285%29+%29%29%2F%282%281%29%29 Square -5 to get 25.


x+=+%285+%2B-+sqrt%28+25-20+%29%29%2F%282%281%29%29 Multiply 4%281%29%285%29 to get 20


x+=+%285+%2B-+sqrt%28+5+%29%29%2F%282%281%29%29 Subtract 20 from 25 to get 5


x+=+%285+%2B-+sqrt%28+5+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%285%2Bsqrt%285%29%29%2F%282%29 or x+=+%285-sqrt%285%29%29%2F%282%29 Break up the expression.


So the solutions are x+=+%285%2Bsqrt%285%29%29%2F%282%29 or x+=+%285-sqrt%285%29%29%2F%282%29


which approximate to x=3.618 or x=1.382


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