Quadratic Equation


This is the derivation of an equation we all know. The equation:

(1)   quicklatex.com-1244d8e1a72131cc104e703414a98f13_l3 Quadratic Equation

As a solution to this:

(2)   quicklatex.com-eee2446419d4adec80029f2b9ab6214f_l3 Quadratic Equation

STEP 1, set the coefficient of the first term to one.

(3)   quicklatex.com-457e010b5a42baac291e850f21f8d41c_l3 Quadratic Equation

STEP 2, Subtract the third term from both sides:

(4)   quicklatex.com-0282a1db39879e74e616d3279331a107_l3 Quadratic Equation

STEP 3, Take one half of the middle term, square it and add to both sides of the equation:

(5)   quicklatex.com-0ce9b683fbdcf3fee2e1f7890ab3b1de_l3 Quadratic Equation

The goal here is to get the left hand term to be a perfect square trinomial. STEP 4. Factor the left hand side of the equation.

(6)   quicklatex.com-abb5a09d0c008dd23d47e04b3e41e4c8_l3 Quadratic Equation

Step 5, Find the least common denominator for the right hand side:

(7)   quicklatex.com-df6bc6b2ccf9e7cfb221f9ab5f18f858_l3 Quadratic Equation

STEP 6, Take the square root of both sides:

(8)   quicklatex.com-1fc3b2b1e9ba822ee59c9d15adc216df_l3 Quadratic Equation

Step 7, Solve for x

(9)   quicklatex.com-48e963cc1238f032124545070f5153ec_l3 Quadratic Equation