1
$\begingroup$

I am stuck trying to solve this equation.

B2(B + 11.97) = 238.67

This is for my math class, we solved this equation and got to that final form and I know that one solution is 3.88 but I don't know how to get it mathematically. I tried using Horner's Method but I don't know how to make it work because 238.67 is not a whole number. Anyone has any ideas or an explanation how to get that 3.88 solution?

$\endgroup$
2
  • $\begingroup$ Why not multiply through both sides by whatever constant necessary to make it a whole number? $\endgroup$ – dalastboss Mar 30 '15 at 23:01
  • $\begingroup$ 3.88 is only an approximate solution. $\endgroup$ – Barry Cipra Mar 30 '15 at 23:03
1
$\begingroup$

You have $$B^2(B + 11.97) = 238.67$$ Rewrite is as $$B^2\Big(B+\frac{1197}{100}\Big)=\frac{23867}{100}$$ Now define $B=\frac{x}{100}$ so the equation becomes $$\frac{x^2}{10000}\Big(\frac{x}{100}+\frac{1197}{100}\Big)=\frac{23867}{100}$$ Multiple by $100$ inside the parentheses and the rhs to get $$\frac{x^2}{10000}(x+{1197})=23867$$ Finally multiply lhs and rhs by $10000$. Use Horner method for an approximate solution of the equation for $x$ and go back to $B$ from $B=\frac{x}{100}$.

$\endgroup$
0
$\begingroup$

Treat it as $B^2(A+11.97)=238.67$ with $A\approx B$ to get a quick estimate, which can be improved with standard methods.

Start by approximating $B^2(A+12)=240$ with $A=0$ so that $B^2\approx 20$ and $B\approx 4$. So set $A=4$ and $B^2\approx 15$ so that $B\approx 3.7$

That's close with no calculator - to get a more accurate solution put the accurate constants in and use a calculator from this point on.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.