Solving Equations
You will generally find the last operation is the first thing to undo. Imagine you are
computing the equation on a calculator. The last operation you would type is likely to be
the first operation to undo. Letâ€™s look at a really big and messy example; try to spot how
weâ€™re working backwards to undo it!
Big Messy Example:
Solve for x: 2(x  1)^{2} + 3 = 21
Solution:
Subtract 3 from both sides: 
2(x  1)^{2} + 3  3 = 21  3 
or: 
2(x  1)^{2} = 18 
Divide both sides by 2: 

or: 
(x  1)^{2} = 9 
Square root of both sides: 

or: 
x  1 = 3 
Finally add 1 to both sides: 
x + 1  1 = 3 + 1 
or: 
x = 4 
Check:
Substitute 4 into the original equation:
2â€¢(41)^{2} + 3 = 21
2â€¢32 + 3 = 21
2â€¢9 + 3 = 21
21 = 21 Yes!
