Algebra 1 Tutorial
Solving Quadratic Equations Using Factoring
A Quadratic Equation at this level usually looks something like this:
2x + 4x – 6 = 0
I will explain the easiest way to solve a quadratic equation.
2x + 4x – 6 = 0
(two x squared plus four x minus six)
2x + 4x – 6 = 0 (ignore the zero until the very end)
1. Take the first number and multiply it with the last number
so: 2 x -6
2. 2 x -6 = -12.
Take -12 and see which two factors that make up twelve can be added together to get the middle number in the equation. In this instance, you can use -2 + 6. These numbers multiplied equal negative twelve, and these numbers added together equal four (four is our middle number).
3. Make the equation look like this now, replacing the 4x with the two numbers that we added to get 4.
so: 2x -2x + 6x -6 = 0
4. Put parentheses around the first two numbers and the last two numbers.
so: (2x -2x) (6x -6)
5. Factor the similar numbers and letters (x) out of these two parentheses parts of the equation. Both of the parts inside of the parentheses should now be the same.
so: 2x(x-1) 6(x-1)
6. Take the numbers outside the parentheses and add them together, and then take the phrase inside of the parentheses. Set both equal to zero.
so: 2x + 6 = 0
x – 1 = 0
7. Solve both these equations, and the answers that you get will be your “zeros,” “x’s,” or your solutions to the quadratic equation.
so: x = -3, x = 1
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