SOLUTION: I need to solve using quadratic formula can you please help? x^2=15+2x

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Question 878981: I need to solve using quadratic formula can you please help?
x^2=15+2x
Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First get everything to one side

x%5E2=15%2B2x

x%5E2-2x=15

x%5E2-2x-15=0

The equation is in the form ax%5E2%2Bbx%2Bc=0 where a+=+1, b+=+-2, c+=+-15

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Use the quadratic formula to solve for x

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

x+=+%28-%28-2%29%2B-sqrt%28%28-2%29%5E2-4%281%29%28-15%29%29%29%2F%282%281%29%29 Plug in a+=+1, b+=+-2, c+=+-15

x+=+%282%2B-sqrt%284-%28-60%29%29%29%2F%282%29

x+=+%282%2B-sqrt%284%2B60%29%29%2F%282%29

x+=+%282%2B-sqrt%2864%29%29%2F2

x+=+%282%2Bsqrt%2864%29%29%2F2 or x+=+%282-sqrt%2864%29%29%2F2

x+=+%282%2B8%29%2F2 or x+=+%282-8%29%2F2

x+=+10%2F2 or x+=+-6%2F2

x+=+5 or x+=+-3

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The two solutions are x+=+5 or x+=+-3

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

x%5E2=15%2B2x
x%5E2-2x-15=0 => the coefficients are: a=1, b=-2, and c=-15
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%5E2-2%2Ax-15=0 ( notice a=1, b=-2, and c=-15)





x+=+%28--2+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A-15+%29%29%2F%282%2A1%29 Plug in a=1, b=-2, and c=-15




x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A-15+%29%29%2F%282%2A1%29 Negate -2 to get 2




x+=+%282+%2B-+sqrt%28+4-4%2A1%2A-15+%29%29%2F%282%2A1%29 Square -2 to get 4 (note: remember when you square -2, you must square the negative as well. This is because %28-2%29%5E2=-2%2A-2=4.)




x+=+%282+%2B-+sqrt%28+4%2B60+%29%29%2F%282%2A1%29 Multiply -4%2A-15%2A1 to get 60




x+=+%282+%2B-+sqrt%28+64+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%282+%2B-+8%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%282+%2B-+8%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%282+%2B+8%29%2F2 or x+=+%282+-+8%29%2F2


Lets look at the first part:


x=%282+%2B+8%29%2F2


x=10%2F2 Add the terms in the numerator

x=5 Divide


So one answer is

x=5




Now lets look at the second part:


x=%282+-+8%29%2F2


x=-6%2F2 Subtract the terms in the numerator

x=-3 Divide


So another answer is

x=-3


So our solutions are:

x=5 or x=-3