SOLUTION: What is a step-by-step way to solve a Quadratic Equation?

Question 234381: What is a step-by-step way to solve a Quadratic Equation?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

There are three methods to solve a quadratic equation. For purposes of this discussion we will presume that the equation to be solved is in standard form, that is:

Factoring

If you can find numbers

, and

such that

, and

, then you can write:

Then, using the Zero Product Rule, that is:

You can say:

Completing The Square

Step 1: Put the equation into standard form, that is:

.

Step 2: Multiply both sides of the equation by the reciprocal of the lead coefficient, that is:

becomes

.

Step 2: Add the additive inverse of the constant term to both sides, that is:

becomes

.

Step 3: Divide the coefficient on the 1st degree term by 2 and then square the result, that is, calculate

.

Step 4: Add the results of step 3 to both sides of the equation, that is:

becomes

Step 5: Factor the perfect square on the left, that is:

becomes

.

Step 6: Take the square root of both sides. Remember to consider both the positive and negative roots, that is:

becomes

.

Step 7: Collect terms and simplify, that is:

becomes

.

The Quadratic Formula

The quadratic formula was derived by completing the square on the general quadratic -- just as was done in the discussion above on completing the square. Take the three coefficients,

, and

and substitute them into the equation found in the last step of the completing the square discussion, namely:

Note that the character of the two roots is indicated by the Discriminant, which is the expression under the radical in the quadratic formula, that is: