SOLUTION: Describe the roots of the equation: 7x^2 + 2x - 3 = 0

Algebra ->  Equations -> SOLUTION: Describe the roots of the equation: 7x^2 + 2x - 3 = 0      Log On


   

Question 110617: Describe the roots of the equation: 7x^2 + 2x - 3 = 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 7%2Ax%5E2%2B2%2Ax-3=0 ( notice a=7, b=2, and c=-3)




x+=+%28-2+%2B-+sqrt%28+%282%29%5E2-4%2A7%2A-3+%29%29%2F%282%2A7%29 Plug in a=7, b=2, and c=-3



x+=+%28-2+%2B-+sqrt%28+4-4%2A7%2A-3+%29%29%2F%282%2A7%29 Square 2 to get 4



x+=+%28-2+%2B-+sqrt%28+4%2B84+%29%29%2F%282%2A7%29 Multiply -4%2A-3%2A7 to get 84



x+=+%28-2+%2B-+sqrt%28+88+%29%29%2F%282%2A7%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-2+%2B-+2%2Asqrt%2822%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+=+%28-2+%2B-+2%2Asqrt%2822%29%29%2F14 Multiply 2 and 7 to get 14

So now the expression breaks down into two parts

x+=+%28-2+%2B+2%2Asqrt%2822%29%29%2F14 or x+=+%28-2+-+2%2Asqrt%2822%29%29%2F14


Now break up the fraction


x=-2%2F14%2B2%2Asqrt%2822%29%2F14 or x=-2%2F14-2%2Asqrt%2822%29%2F14


Simplify


x=-1+%2F+7%2Bsqrt%2822%29%2F7 or x=-1+%2F+7-sqrt%2822%29%2F7


So these expressions approximate to

x=0.527202251403347 or x=-0.812916537117633


So our solutions are:
x=0.527202251403347 or x=-0.812916537117633

Notice when we graph 7%2Ax%5E2%2B2%2Ax-3, we get:



when we use the root finder feature on a calculator, we find that x=0.527202251403347 and x=-0.812916537117633.So this verifies our answer