How to solve Quadratic equations that are not factorable
There are two ways we can solve this. By using "completing the square" and using the Quadratic Formula.
COMPLETING the SQUARE
Let's first recall the PST or Perfect Square Trinomial
--> a^2 + 2ab + b^2 or a^2 - 2ab + b^2
solving:
*first, write the equation: for example
2x^2 +12x - 3 = 0
* divide the entire equation by the leading coefficient
x^2 +6x - 3/2 = 0
* move the constant term to the right side. Remember that the signs will change.
x^2 + 6x = 3/2
* half of the x-term's coefficient squared. Add the value to the both side of equation.
x^2 + 6x+ 9 = 3/2 + 9
*Now the left side is perfect square, factor it then get the square root of both sides.
*simplify.
COMPLETING the SQUARE
Let's first recall the PST or Perfect Square Trinomial
--> a^2 + 2ab + b^2 or a^2 - 2ab + b^2
solving:
*first, write the equation: for example
2x^2 +12x - 3 = 0
* divide the entire equation by the leading coefficient
x^2 +6x - 3/2 = 0
* move the constant term to the right side. Remember that the signs will change.
x^2 + 6x = 3/2
* half of the x-term's coefficient squared. Add the value to the both side of equation.
x^2 + 6x+ 9 = 3/2 + 9
*Now the left side is perfect square, factor it then get the square root of both sides.
*simplify.