SOLUTION: I am trying to solve x^2+14x=5. I make it to the middle of the problem and then get lost. Please help!

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Question 476476: I am trying to solve x^2+14x=5.
I make it to the middle of the problem and then get lost. Please help!

Found 3 solutions by jim_thompson5910, Edwin McCravy, MathLover1:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B14x=5 Start with the given equation.


x%5E2%2B14x-5=0 Get every term to the left side.


For more help, check out this quadratic formula solver.

Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2%2B14%2Ax-5=0 ( notice a=1, b=14, and c=-5)





x+=+%28-14+%2B-+sqrt%28+%2814%29%5E2-4%2A1%2A-5+%29%29%2F%282%2A1%29 Plug in a=1, b=14, and c=-5




x+=+%28-14+%2B-+sqrt%28+196-4%2A1%2A-5+%29%29%2F%282%2A1%29 Square 14 to get 196




x+=+%28-14+%2B-+sqrt%28+196%2B20+%29%29%2F%282%2A1%29 Multiply -4%2A-5%2A1 to get 20




x+=+%28-14+%2B-+sqrt%28+216+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-14+%2B-+6%2Asqrt%286%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-14+%2B-+6%2Asqrt%286%29%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%28-14+%2B+6%2Asqrt%286%29%29%2F2 or x+=+%28-14+-+6%2Asqrt%286%29%29%2F2



Now break up the fraction



x=-14%2F2%2B6%2Asqrt%286%29%2F2 or x=-14%2F2-6%2Asqrt%286%29%2F2



Simplify



x=-7%2B3%2Asqrt%286%29 or x=-7-3%2Asqrt%286%29



So the solutions are:

x=-7%2B3%2Asqrt%286%29 or x=-7-3%2Asqrt%286%29





For more help, check out this quadratic formula solver.

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B14x=5

x%5E2%2B14x-5=0

a=1, b=14, c=-5

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ 

x+=+%28-14+%2B-+sqrt%28+14%5E2-4%2A1%2A%28-5%29+%29%29%2F%282%2A1%29+

x+=+%28-14+%2B-+sqrt%28196%2B20%29+%29%2F2+

x+=+%28-14+%2B-+sqrt%28196%2B20%29+%29%2F2+
 
x+=+%28-14+%2B-+sqrt%28216%29+%29%2F2+

x+=+%28-14+%2B-+sqrt%2836%2A6%29+%29%2F2+

x+=+%28-14+%2B-+6sqrt%286%29+%29%2F2+

x+=+%282%28-7+%2B-+3sqrt%286%29+%29%29%2F2+

x+=+%28cross%282%29%28-7+%2B-+3sqrt%286%29+%29%29%2Fcross%282%29+

x+=+-7+%2B-+3sqrt%286%29+%29+

Edwin

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B14x=5
x%5E2%2B14x-5=0...in order to solve for x, we need to use the quadratic formula

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+...note: a=1, b=14 and c=-5

x+=+%28-14+%2B-+sqrt%28+14%5E2-4%2A1%2A%28-5%29+%29%29%2F%282%2A1%29+

x+=+%28-14+%2B-+sqrt%28+196%2B20+%29%29%2F2+

x+=+%28-14+%2B-+sqrt%28+216%29%29%2F2+

x+=+%28-14+%2B-+14.7%29%2F2+

solutions:

x+=+%28-14+%2B+14.7%29%2F2+
x+=+%280.7%29%2F2+
x+=+0.35+
or
x+=+%28-14+-+14.7%29%2F2+
x+=+%28-28.7%29%2F2+
x+=+-14.35+

check:
x%5E2%2B14x=5...plug in x+=+0.35+

%280.35%29%5E2%2B14%280.35%29=5
0.1225%2B4.9=5
5.0225=5.....round
5=5