Quadratic Equation


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

(1)   quicklatex.com-6aa71217898194c1efa2d180d5bca1c9_l3 Quadratic Equation

As a solution to this:

(2)   quicklatex.com-ce1bcd6f67127814482be905ee296df6_l3 Quadratic Equation

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

(3)   quicklatex.com-a2013b9dc32e982bf12beb5c48848f69_l3 Quadratic Equation

STEP 2, Subtract the third term from both sides:

(4)   quicklatex.com-3f93f5035e6500a67c9c4e99b2e0dee8_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-db24c15261a191d050bd63cc587c52f1_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-8f40be772ba014081ecbe5d2a63881ee_l3 Quadratic Equation

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

(7)   quicklatex.com-d0c089c123a550e3d8850b4e96f9a3bd_l3 Quadratic Equation

STEP 6, Take the square root of both sides:

(8)   quicklatex.com-7cc8f51d58c8f8556a052fe29895464e_l3 Quadratic Equation

Step 7, Solve for x

(9)   quicklatex.com-e50d1691f6fd4cdf2a5cb77402c1b146_l3 Quadratic Equation