# Solve equation using Horner's Method.

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?

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

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 $B=\frac{x}{100}$.
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 $B\approx 3.7$