SOLUTION: Most quadratic eqautions Ive come across so far have given the problem as something equals 0 format. This one below is the first Ive seen in this format so its got me scratching my

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Most quadratic eqautions Ive come across so far have given the problem as something equals 0 format. This one below is the first Ive seen in this format so its got me scratching my      Log On


   

Question 98447: Most quadratic eqautions Ive come across so far have given the problem as something equals 0 format. This one below is the first Ive seen in this format so its got me scratching my head.
Use the quadratic equation to solve: 6n^2= -8n-1
Give the answer in decimal form.
This neither has the equals 0 as a start point or ask me what to solve for. It just says solve. Help please.
Thank you.
Found 3 solutions by mathslover, jim_thompson5910, edjones:
Answer by mathslover(157) About Me  (Show Source):
You can put this solution on YOUR website!
Given equation
6n^2= -8n-1
add 8n +1 on both sides
6n^2 + 8n + 1 =0 ( looks more familiar now ?)
use the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
n=+%28-8+%2B-+sqrt%288%5E2+-+4%2A6%2A1%29%29%2F%282%2A6%29
n=+%28-8+%2B-+sqrt%2864+-+24%29%29%2F12
n=+%28-8+%2B-+sqrt%2840%29%29%2F12
n=+%28-8+%2B-+6.325+%29%2F12%29
n= -1.193 and n= -0.1396

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Well if it's not in the "equals 0" format, you must get all terms to one side


6n%5E2=+-8n-1 Start with the given quadratic


0=+-6n%5E2-8n-1 Subtract 6n%5E2 from both sides to get all terms to one side. Now one side equals zero



Let's use the quadratic formula to solve for n:


Starting with the general quadratic

an%5E2%2Bbn%2Bc=0

the general solution using the quadratic equation is:

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

So lets solve -6%2An%5E2-8%2An-1=0 ( notice a=-6, b=-8, and c=-1)

n+=+%28--8+%2B-+sqrt%28+%28-8%29%5E2-4%2A-6%2A-1+%29%29%2F%282%2A-6%29 Plug in a=-6, b=-8, and c=-1



n+=+%288+%2B-+sqrt%28+%28-8%29%5E2-4%2A-6%2A-1+%29%29%2F%282%2A-6%29 Negate -8 to get 8



n+=+%288+%2B-+sqrt%28+64-4%2A-6%2A-1+%29%29%2F%282%2A-6%29 Square -8 to get 64 (note: remember when you square -8, you must square the negative as well. This is because %28-8%29%5E2=-8%2A-8=64.)



n+=+%288+%2B-+sqrt%28+64%2B-24+%29%29%2F%282%2A-6%29 Multiply -4%2A-1%2A-6 to get -24



n+=+%288+%2B-+sqrt%28+40+%29%29%2F%282%2A-6%29 Combine like terms in the radicand (everything under the square root)



n+=+%288+%2B-+2%2Asqrt%2810%29%29%2F%282%2A-6%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



n+=+%288+%2B-+2%2Asqrt%2810%29%29%2F-12 Multiply 2 and -6 to get -12

So now the expression breaks down into two parts

n+=+%288+%2B+2%2Asqrt%2810%29%29%2F-12 or n+=+%288+-+2%2Asqrt%2810%29%29%2F-12


Now break up the fraction


n=%2B8%2F-12%2B2%2Asqrt%2810%29%2F-12 or n=%2B8%2F-12-2%2Asqrt%2810%29%2F-12


Simplify


n=-2+%2F+3-sqrt%2810%29%2F6 or n=-2+%2F+3%2Bsqrt%2810%29%2F6


So these expressions approximate to

n=-1.1937129433614 or n=-0.139620389971937


So our solutions are:
n=-1.1937129433614 or n=-0.139620389971937

Notice when we graph -6%2Ax%5E2-8%2Ax-1 (just replace n with x), we get:



when we use the root finder feature on a calculator, we find that x=-1.1937129433614 and x=-0.139620389971937.So this verifies our answer

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
add 8n+1 to both sides. 6n^2+8n+1=0
How about that?
It doesn't factor.
Use the quadratic equation.
Ed