The Quadratic Formula Proof

The solution to the quadratic equation (a≠0)
, which we call the Quadratic Formula .

PROOF

	Start with the quadratic equation, then Subtract c from both sides of the equation
	Divide both sides of the equation by a
	Simplify
	Now Complete the Square in x
then	Take ½ of the coefficient of x , then square this result, then add to both sides of the equation.
	Get a common denominator on the right hand side of the equation
	Combine the two fractions on the right
	Now FACTOR the left hand side of the equation, which is a perfect square trinomial
	Take the Square Root of both sides of the equation

	Note:
	Break the Absolute Value into 2 Cases : ±
	Break the radical into 2 radicals
	Simplify the radical in the denominator
	As sume that a > 0 to remove the absolute value. If a < 0 , then divide both sides of the equation by – 1 at the start of the problem to make a > 0
	Subtract from both sides of the equation
	Combine the fractions

End Of Proof

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