SOLUTION: solve x^2+14x-4=0 the solution I get is two not sure which one is correct can you help? =-7+√53, -7-√53 or 7+√53,7-√53?

Algebra ->  Rational-functions -> SOLUTION: solve x^2+14x-4=0 the solution I get is two not sure which one is correct can you help? =-7+√53, -7-√53 or 7+√53,7-√53?      Log On


   

Question 475594: solve x^2+14x-4=0 the solution I get is two not sure which one is correct can you help?
=-7+√53, -7-√53 or 7+√53,7-√53?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B14x-4=0 Start with the given equation.


Notice that the quadratic x%5E2%2B14x-4 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%28-4%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%28-4%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%28-4%29 to get -16


x+=+%28-14+%2B-+sqrt%28+196%2B16+%29%29%2F%282%281%29%29 Rewrite sqrt%28196--16%29 as sqrt%28196%2B16%29


x+=+%28-14+%2B-+sqrt%28+212+%29%29%2F%282%281%29%29 Add 196 to 16 to get 212


x+=+%28-14+%2B-+sqrt%28+212+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-14+%2B-+2%2Asqrt%2853%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-+%282%2Asqrt%2853%29%29%2F%282%29 Break up the fraction.


x+=+-7+%2B-+sqrt%2853%29 Reduce.


x+=+-7%2Bsqrt%2853%29 or x+=+-7-sqrt%2853%29 Break up the expression.


So the solutions are x+=+-7%2Bsqrt%2853%29 or x+=+-7-sqrt%2853%29