Problem of the Week

Updated at Apr 14, 2025 5:50 PM

This week's problem comes from the equation category.

How would you solve 2(3−t2)3−t=26\frac{2(3-{t}^{2})}{3-t}=26?

Let's begin!



2(3−t2)3−t=26\frac{2(3-{t}^{2})}{3-t}=26

1
Multiply both sides by 3−t3-t.
2(3−t2)=26(3−t)2(3-{t}^{2})=26(3-t)

2
Divide both sides by 22.
3−t2=13(3−t)3-{t}^{2}=13(3-t)

3
Expand.
3−t2=39−13t3-{t}^{2}=39-13t

4
Move all terms to one side.
3−t2−39+13t=03-{t}^{2}-39+13t=0

5
Simplify  3−t2−39+13t3-{t}^{2}-39+13t  to  −36−t2+13t-36-{t}^{2}+13t.
−36−t2+13t=0-36-{t}^{2}+13t=0

6
Multiply both sides by −1-1.
t2−13t+36=0{t}^{2}-13t+36=0

7
Factor t2−13t+36{t}^{2}-13t+36.
(t−9)(t−4)=0(t-9)(t-4)=0

8
Solve for tt.
t=9,4t=9,4

Done
Cymath foriOSAndroid