Respuesta :
Answer:
r=−9.403283,−6.348173,0.751456
Step-by-step explanation:
Let's solve your equation step-by-step.
7(r3+15r2+48r−44)=r+6
7r3+105r2+336r−308=r+6
Step 1: Subtract r+6 from both sides.
7r3+105r2+336r−308−(r+6)=r+6−(r+6)
7r3+105r2+335r−314=0
Step 2: Use cubic formula.
r=−9.403283,−6.348173,0.751456
Answer:
[tex]\frac{-178 + and - \sqrt{64654} }{105}[/tex]
Step-by-step explanation:
Advanced equations like these fit perfect to do the quadratic formula
first we must find a,b and c
A=[tex]x^{2}[/tex]
B=constant multiplied by x
C=constant not multiplied by x
Alright now that we established that we need to format the equation to equal 0 so it will basically look like this [tex]a^{2}[/tex]+b+c=0
First add like terms
7 (51r + [tex]15^{2}[/tex] -44) = r + 6
Then we do the distributive property
357r + [tex]105r^{2}[/tex] -308 = r + 6
Then we inverse the R + 6 so we can make the equation equal 0
so 357r + [tex]105r^{2}[/tex] -308-r-6 = 0
Add like terms again
356r + [tex]105r^{2}[/tex] -314=0
Now we have our A B and C!!! So lets put it in the quadratic formula
I like to find the discriminant first which is [tex]b^{2} -4ac[/tex] so lets plug everything in.
356[tex]356^{2} -4(105)(-314)[/tex]
and that equals
258616 but that isn't a perfect square so we'll need to factor it so lets keep it fragmented for the time being
[tex]\frac{-316+ and -\sqrt{356^{2}+131880 } }{210}[/tex]
is our current expression
The easiest thing to factor out is [tex]2^{2}[/tex]
So that should equal
[tex]\frac{-356+ and -\sqrt{2^{2} *64654} }{210}[/tex]
Square [tex]2^{2}[/tex]
[tex]\frac{-356+and-2\sqrt{64654} }{210}[/tex]
now the only thing left to do is divided every thing by the greatest common factor which is 2, we don't divided whatever is in the [tex]\sqrt{x}[/tex] when doing this step
so the final solution is
[tex]\frac{-178+ and -\sqrt{64654} }{105}[/tex]
