SOLUTION: x^2-48=0

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Question 96856: x^2-48=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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%5E2-48=0 (note: since the polynomial does not have an "x" term, the 2nd coefficient is zero. In other words, b=0. So that means the polynomial really looks like x%5E2%2B0%2Ax-48=0 notice a=1, b=0, and c=-48)

x+=+%280+%2B-+sqrt%28+%280%29%5E2-4%2A1%2A-48+%29%29%2F%282%2A1%29 Plug in a=1, b=0, and c=-48



x+=+%280+%2B-+sqrt%28+0-4%2A1%2A-48+%29%29%2F%282%2A1%29 Square 0 to get 0



x+=+%280+%2B-+sqrt%28+0%2B192+%29%29%2F%282%2A1%29 Multiply -4%2A-48%2A1 to get 192



x+=+%280+%2B-+sqrt%28+192+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%280+%2B-+8%2Asqrt%283%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+=+%280+%2B-+8%2Asqrt%283%29%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%280+%2B+8%2Asqrt%283%29%29%2F2 or x+=+%280+-+8%2Asqrt%283%29%29%2F2


Now break up the fraction


x=0%2F2%2B8%2Asqrt%283%29%2F2 or x=0%2F2-8%2Asqrt%283%29%2F2


Simplify


x=4%2Asqrt%283%29 or x=-4%2Asqrt%283%29


So these expressions approximate to

x=6.92820323027551 or x=-6.92820323027551


So our solutions are:
x=6.92820323027551 or x=-6.92820323027551

Notice when we graph x%5E2-48, we get:



when we use the root finder feature on a calculator, we find that x=6.92820323027551 and x=-6.92820323027551.So this verifies our answer