Quadratic Equations: Quadratic Formula .how to derive the general formular /almighty formular

The Quadratic Formula. The quadratic equation

has the solutions
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Consider the general quadratic equation

with . First divide both sides of the equation by a to get

which leads to

Next complete the square by adding to both sides

Finally we take the square root of both sides:

or

We call this result the Quadratic Formula and normally write it

Remark. The plus-minus sign states that you have two numbers and .

Example: Use the Quadratic Formula to solve

Solution. We have a=2, b= -3, and . By the quadratic formula, the solutions are

Please go to General Conclusion to find a summary of all the cases regarding the roots of a quadratic equation.