SOLUTION: Hello, I have a problem that I am working on but I have two answers. Can someone tell me what I am doing wrong. The problem is: solve by x: x^2+14x+4=0 my first answer i

Algebra ->  Equations -> SOLUTION: Hello, I have a problem that I am working on but I have two answers. Can someone tell me what I am doing wrong. The problem is: solve by x: x^2+14x+4=0 my first answer i      Log On


   

Question 460081: Hello,
I have a problem that I am working on but I have two answers. Can someone tell me what I am doing wrong. The problem is:
solve by x: x^2+14x+4=0
my first answer is: 7sqrt 5, 7-sqrt 5
my second answer is: -7-3 sqrt 5, 3 sqrt 7
I am so lost, please help. Thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B14x%2B4=0 Start with the given equation.


Notice that the quadratic x%5E2%2B14x%2B4 is in the form of Ax%5E2%2BBx%2BC where A=1, B=14, and C=4


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-%2814%29+%2B-+sqrt%28+%2814%29%5E2-4%281%29%284%29+%29%29%2F%282%281%29%29 Plug in A=1, B=14, and C=4


x+=+%28-14+%2B-+sqrt%28+196-4%281%29%284%29+%29%29%2F%282%281%29%29 Square 14 to get 196.


x+=+%28-14+%2B-+sqrt%28+196-16+%29%29%2F%282%281%29%29 Multiply 4%281%29%284%29 to get 16


x+=+%28-14+%2B-+sqrt%28+180+%29%29%2F%282%281%29%29 Subtract 16 from 196 to get 180


x+=+%28-14+%2B-+sqrt%28+180+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-14+%2B-+6%2Asqrt%285%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-14%29%2F%282%29+%2B-+%286%2Asqrt%285%29%29%2F%282%29 Break up the fraction.


x+=+-7+%2B-+3%2Asqrt%285%29 Reduce.


x+=+-7%2B3%2Asqrt%285%29 or x+=+-7-3%2Asqrt%285%29 Break up the expression.


So the solutions are x+=+-7%2B3%2Asqrt%285%29 or x+=+-7-3%2Asqrt%285%29