The first and simplest way to solve many equations is to factor them. How does this help? you ask. First you have to set the equation equal to zero by moving all of the terms over to one side. Example: x² = 49. Move the 49 over: x² - 49 = 0 and you're ready to factor. Factor the equation into (x - 7)(x + 7) = 0. Then comes the trick. Because the equation equals zero, one of the two factors equals zero. In simpler terms take (x)(y) = 0 one of these equals zero because multiplying something by zero is the only way to get zero in multiplication. Thus x = 0 OR y = 0. Looking back on our old practice problem, we can see that x - 7 = 0 OR x + 7 = 0. Solve these and you get that x = 7 OR x = -7 and is written as x = ±7. Easy isn't it!
Example 2: 3x² + 2 = -7x
Bring the -7x over : 3x² + 7x + 2 = 0
Factor: (3x + 1)(x + 2) = 0
Set both expressions to zero: 3x + 1 = 0 OR x + 2 = 0
Solve: x = -(1/3) OR x = -2
This shows the 5 simple steps to solving factorable quadratics:
1. Set the equation equal to zero (Bring extra terms over)
2. Factor
3. Set all expressions equal to zero
4. Solve
5. Simplify