# What is the formula used for to solve quadratice problems and what is the quickess and/ or most accurate way to solve a solution?

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Expert Answers

crmhaske | Certified Educator

The formula that can be used to solve for the roots of a quadratic equation is as follows:

`x=(-b+-sqrt(b^2-4ac))/(2a)`

Where, a, b, and c are taken from the standard form of a quadratic equation:

`ax^2+bx+c`

As it eliminates the need for trial and error with other methods of solving for a quadratic (such as factoring), it is the most efficient method for solving a quadratic equation.

It is arrived at by completing the square:

`ax^2+bx+c=0`

`x^2+b/ax+c/a=0`

`(x+b/(2a))^2+c/a-(b/(2a))^2=0`

`(x+b/(2a))^2=-c/a+b^2/(4a^2)`

`(x+b/(2a))^2=(b^2-4ac)/(4a^2)`

`x+b/(2a)=+-sqrt(b^2-4ac)/(2a)`

`x=(-b+-sqrt(b^2-4ac))/(2a)`

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