Question 1

How do I solve a formula for a variable when the other values are unknown?

Accepted Answer

Treat every letter except the target as a constant. You can add, subtract, multiply, divide, or factor exactly as with numbers; the answer is an expression instead of a single value.

Question 2

What do I do when the target variable appears in two terms?

Accepted Answer

Move every term containing it to one side, factor the variable out, and divide both sides by whatever is left in the parentheses. Factoring is the one genuinely new step here.

Question 3

How do I isolate a variable that is squared or under a root?

Accepted Answer

Undo the outer operation last. Squared: isolate the square, then take ±√() of both sides. Under a root: isolate the root, then square both sides.

Question 4

Do I clear fractions the same way?

Accepted Answer

Yes — multiply every term by the LCD, or multiply both sides by the reciprocal of a single fractional coefficient.

Question 5

When do I worry about dividing by zero?

Accepted Answer

Whenever you divide both sides by an expression containing a variable, that expression is assumed nonzero. Most formulas guarantee this; note it when the divisor could plausibly be zero.

Question 6

Does my rearranged formula have to match the solution exactly?

Accepted Answer

No — only algebraically. The checker evaluates your expression and the correct one at many random values instead of comparing text, so (A-P)/(P*r), (A - P)/(Pr) and t = (A-P)/(P r) all pass. Use / for division, * or nothing for multiplication, and sqrt() for a root.

Solving for a Variable Practice Problems