SOLUTION: x^2+14x-31=0

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Question 200025This question is from textbook Algebra 2
: x^2+14x-31=0 This question is from textbook Algebra 2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B14x-31=0 Start with the given equation.


Notice that the quadratic x%5E2%2B14x-31 is in the form of Ax%5E2%2BBx%2BC where A=1, B=14, and C=-31


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%28-31%29+%29%29%2F%282%281%29%29 Plug in A=1, B=14, and C=-31


x+=+%28-14+%2B-+sqrt%28+196-4%281%29%28-31%29+%29%29%2F%282%281%29%29 Square 14 to get 196.


x+=+%28-14+%2B-+sqrt%28+196--124+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-31%29 to get -124


x+=+%28-14+%2B-+sqrt%28+196%2B124+%29%29%2F%282%281%29%29 Rewrite sqrt%28196--124%29 as sqrt%28196%2B124%29


x+=+%28-14+%2B-+sqrt%28+320+%29%29%2F%282%281%29%29 Add 196 to 124 to get 320


x+=+%28-14+%2B-+sqrt%28+320+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-14+%2B-+8%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-+%288%2Asqrt%285%29%29%2F%282%29 Break up the fraction.


x+=+-7+%2B-+4%2Asqrt%285%29 Reduce.


x+=+-7%2B4%2Asqrt%285%29 or x+=+-7-4%2Asqrt%285%29 Break up the expression.


So the solutions are x+=+-7%2B4%2Asqrt%285%29 or x+=+-7-4%2Asqrt%285%29


which approximate to x=1.944 or x=-15.944