SOLUTION: x=1-7x^2

Algebra ->  Human-and-algebraic-language -> SOLUTION: x=1-7x^2      Log On


   

Question 115403: x=1-7x^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x=1-7x%5E2 Start with the given equation


7x%5E2%2Bx-1=0 Move all of the terms to the left side


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 7%2Ax%5E2%2Bx-1=0 ( notice a=7, b=1, and c=-1)




x+=+%28-1+%2B-+sqrt%28+%281%29%5E2-4%2A7%2A-1+%29%29%2F%282%2A7%29 Plug in a=7, b=1, and c=-1



x+=+%28-1+%2B-+sqrt%28+1-4%2A7%2A-1+%29%29%2F%282%2A7%29 Square 1 to get 1



x+=+%28-1+%2B-+sqrt%28+1%2B28+%29%29%2F%282%2A7%29 Multiply -4%2A-1%2A7 to get 28



x+=+%28-1+%2B-+sqrt%28+29+%29%29%2F%282%2A7%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-1+%2B-+sqrt%2829%29%29%2F%282%2A7%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-1+%2B-+sqrt%2829%29%29%2F14 Multiply 2 and 7 to get 14

So now the expression breaks down into two parts

x+=+%28-1+%2B+sqrt%2829%29%29%2F14 or x+=+%28-1+-+sqrt%2829%29%29%2F14


Now break up the fraction


x=-1%2F14%2Bsqrt%2829%29%2F14 or x=-1%2F14-sqrt%2829%29%2F14


Simplify


x=-1+%2F+14%2Bsqrt%2829%29%2F14 or x=-1+%2F+14-sqrt%2829%29%2F14


So these expressions approximate to

x=0.313226057652465 or x=-0.456083200509607


So our solutions are:
x=0.313226057652465 or x=-0.456083200509607

Notice when we graph 7%2Ax%5E2%2Bx-1, we get:



when we use the root finder feature on a calculator, we find that x=0.313226057652465 and x=-0.456083200509607.So this verifies our answer