Quadratic Equations - Mathematics and Statistics for the Environment - page 100

5.4 USING THE QUADRATIC EQUATION

■ EXAMPLE 5.3
Problem: After conducting a study and deriving an equation representing time, we arrive at the
following equation:

x 2 = 5 x + 6 = 0

Solution: All like terms have been combined and the equation is set to equal zero. Use the quadratic
formula to solve the problem:

2

= −± −

bb ac
a

4

x

2

From our equation, a = 1 (the coefficient of x 2 ), b = -5 (the coefficient of x ), and c = 6 (the constant
or third term). Substituting these coefficients in the quadratic formula:

2

= −− ±−−

() () 5 5 41 6 ()()

x

21 ()

= ±−

5 54
2
51
2

x

±

x =

x = 3 ,, 2

Note: The roots may not always be rational (integers), but the procedure is the same.

REFERENCES AND RECOMMENDED READING
Bourne, M. (2013). Quadratic Equations . Interactive Mathematics, http://www.intmath.com/quadratic-equa-
tions/quadratic-equations-intro.php.