Wednesday, March 27, 2013

 Although we can solve quadratic equations by completing the square, sometimes this process is cumbersome and a bit difficult. There is a simpler way to solve quadratic equations through the use of the quadratic formula.The quadratic formula is found by completing the square of a quadratic equation in the form ax^2 + bx + c = 0, a > 0.

ax^2 + bx + c = 0
ax^2 + bx = -c (Subtract c from both sides of the equation)
x^2 + (b/a)x = -c/a (Divide both sides of the equation by a)
x^2 + (b/a)x + b^2/(4a^2) = -c/a + b2/(4a^2) (Complete the square by taking half of (b/a) , squaring it and adding to both sides)
[x + (b/2a)]^2 = -c/a + b^2/(4a^2) (Factor the perfect square trinomial on the left side)
[x + (b/2a)]^2 = (b^2 – 4ac)/4a^2 (Get common denominator of 4a^2 on the right side)
x + (b/2a) = +/- √[(b^2 – 4ac)/4a^2] (Take the square root of both sides (use the square root property))
x + (b/2a) = +/- √(b^2 – 4ac)/2a (Simplify the square root on the right side √(4a^2) = 2a)
x = [-b +/- √(b^2 – 4ac)]/2a (Subtract b/2a from both sides)

The result is known as the quadratic formula

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