The Quadratic Formula
Completing the square provides a reliable approach to solving quadratic equations, but you can also use an approach that involves applying the quadratic formula. To use the quadratic formula, you first put the equation you are dealing with in a standard form. As mentioned before, the standard form of a quadratic equation is as follows:
ax2 + bx + c = 0
It is not absolutely necessary that you set up the equation in this way, but if you do, then it becomes easier to use the quadratic formula to work with it. The quadratic formula is stated as follows:
Consider the following quadratic equation:
2x2 + 3x = 7
To rewrite the equation in standard form, you add –7 to both sides:
2x2 + 3x – 7 = 0
You can then identify a, b, and c as follows: a = 2, b = 3, and c =–7.
Substituting these values into the quadratic formula, you arrive at this equation:
For a solution set, you can use a calculator to arrive at a decimal value that represents the root or an approximation of the root:
