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GB-41-06-001 · Rearranging with powers

Make r the subject of V=10r2+1V=10r^2+1, where r ≥ 0.

Rearranging Formula: Subject Appears Once ("Story of r") Booklet p. 28
Method
1) Write the Story of r (square → ×a → +b)
2) Apply inverse operations in reverse order (−b → ÷a → √)
Worked Example (GB-41-06-001)
V=10r2+1V = 10r^2 + 1
← 1) Kill +1+1
−1-1 −1-1
V−1=10r2V - 1 = 10r^2
← 2) Kill ×10\times 10
÷10\div 10 ÷10\div 10
V−110=r2\frac{V - 1}{10} = r^2
← 3) Kill square
\sqrt{\quad} \sqrt{\quad}
r=V−110r=\sqrt{\frac{V-1}{10}}
Story of rr
Forward ↓
rr
square (2)\text{square } (^2)
×10\times 10
+1+ 1
Kill (Reverse ↑)
−1- 1
÷10\div 10
\sqrt{\quad}