Solve the formula for the indicated variable.

Question

 

 

1.  Quadratic Formula: ax² + bx + c = 0, for b 

 

2. Pythagorean Theorem: a² + b² = c², for a

 

3. Formula for the surface area of a cone: S=3.14rs+3.14r², for s

Answer 1

What this means is that we need to isolate the specific variable:

 

1

ax² + bx + c = 0

subtract the other terms to the other side:

bx = -ax² - c

Divide by x:

b = (-ax² - c) / x

If you want, you can factor out the negative sign:

b = -(ax² + c) / x

 

2

a2 + b2 = c2

subtract out the other term:

a² = c² - b²

Square root:

a = ±√(c² - b²)

 

Why the plus/minus sign? Because:

4² = 16

(-4)² = 16

 

3

S = 3.14rs + 3.14r²

Subtract the other term from both sides:

S - 3.14r² = 3.14rs

Divide both sides by everything not s in its term:

(S - 3.14r²) / 3.14r = s