SOLUTION: Hi, I am having a real hard time trying to figure out this equation. I can not seem to find any kind of example that comes close enough to help me. I have a test tomorrow and this

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Hi, I am having a real hard time trying to figure out this equation. I can not seem to find any kind of example that comes close enough to help me. I have a test tomorrow and this       Log On


   

Question 323274: Hi, I am having a real hard time trying to figure out this equation. I can not seem to find any kind of example that comes close enough to help me. I have a test tomorrow and this is an example of what the test is about. Here is the equation.
What are the solutions? 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%5E2-5x%2B3=0 Start with the given equation.


Notice that the quadratic x%5E2-5x%2B3 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-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%281%29%283%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-5, and C=3


x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%281%29%283%29+%29%29%2F%282%281%29%29 Negate -5 to get 5.


x+=+%285+%2B-+sqrt%28+25-4%281%29%283%29+%29%29%2F%282%281%29%29 Square -5 to get 25.


x+=+%285+%2B-+sqrt%28+25-12+%29%29%2F%282%281%29%29 Multiply 4%281%29%283%29 to get 12


x+=+%285+%2B-+sqrt%28+13+%29%29%2F%282%281%29%29 Subtract 12 from 25 to get 13


x+=+%285+%2B-+sqrt%28+13+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%285%2Bsqrt%2813%29%29%2F%282%29 or x+=+%285-sqrt%2813%29%29%2F%282%29 Break up the expression.


So the solutions are x+=+%285%2Bsqrt%2813%29%29%2F%282%29 or x+=+%285-sqrt%2813%29%29%2F%282%29


which approximate to x=4.303 or x=0.697