How do you use the quadratic formula?

The quadratic formula is ax² + bx + c = 0. To solve for x, you must get it on one side: x = [ -b ± sqrt(b² - 4ac) ] / 2a. Start by filling in all of the known variables. Calculate the answer.

1. Write down the equation

   Write down the equation and the problem being solved. ax² + bx + c = 0 x = [ -b ± sqrt(b² - 4ac) ] / 2a for the problem x² + 3x - 9 = 0

2. Fill in known variables

   The next step is filling in all of the known variables, which are a, b and c. The variables a, b and c are the coefficients of each respective term. In the example x² + 3x - 9 = 0, a equals 1, b equals 3, and c equals -9. In quadratic form, that looks like: x = [ -3 ± sqrt(3² - 4(1)(-9)] / 2(1).

3. Start solving

   Use the order of operations: parentheses, exponents, multiplication, division, addition and subtraction (PEMDAS) to start solving the problem. These operations must be used in the specified order. Start with the parentheses first and complete all the operations within the parentheses/brackets.
   
   x = [ -3 ± sqrt(3² - 4(1)(-9)] / 2(1)
   x = [ -3 ± sqrt(9 - 4(-9)] / 2(1)
   x = [ -3 ± sqrt(9 + 36)] / 2(1)
   x = [ -3 ± sqrt(45)] / 2(1)
   x = [ -3 ± 6.7] / 2(1)
   x = 3.7 / 2(1) AND x = 9.7 / 2(1)
   
   Then, use PEMDAS for the rest of the equation outside the parentheses.
   
   x = 3.7 / 2 AND x = -9.7 / 2
   x = 1.85 AND x = -4.85