Question 320743
1) The Principle of Zero Prducts states:
If A*B = 0, then either A = 0, or B = 0, or both A and B are 0.
In solving quadratic equations by factoring, you typically end up with two binomial factors whose product equals zero; for example...
{{{x^2+25x-84 = 0}}} and, when factored you get:
{{{(x-3)(x+28) = 0}}} Applying the principle of Zero Products, you can state that...
{{{x-3 = 0}}} or {{{x+28 = 0}}} from which follows...
{{{x = 3}}} or {{{x = -28}}}
2) To complete the square of {{{x^2+14x = 0}}} you will add the square of half the x-coefficient to both sides of the equation, thus...
{{{x^2+14x+(14/2)^2 = 0+(14/2)^2}}} Simplifying this you get...
{{{x^2+14x+49 = 7^2}}} Factoring the left side gives you...
{{{(x+7)^2 = 7^2}}} which is readily solved by taking the square root of both sides and solving for x.
{{{x+7 = 7}}} or {{{x+7 = -7}}} so that...
{{{x = 0}}} or {{{x = -14}}}