Algebra Demystified 2nd Ed

382 alGEbra De mystif ieD

13 14 10

13 110

13 10 10

xx^2

xx

xx

++=

++=

+= +=

()()

−− 11    −− 11 

13

x==− =− 11  xxButl=− 1 eads toazero

inadenominator,so

x= 13 −^1 xn=− 1 is ottasolution.

Summary

In this chapter, we learned how to:

•   Write quadratic equations in the form ax^2 ++=bx c^0

•   Solve quadratic equations by factoring. Once the equation is written in the

above form, we factor the nonzero side, set each factor equal to 0, and

then solve for x.

•   Solve a quadratic equation with the quadratic formula. The quadratic formula

x bbac

a

=−± −

(^24)
2
solves every quadratic equation. Once we identify a, b,
and c, we put these values in the formula and then perform the arithmetic.
• Simplify an equation to make factoring and using the quadratic formula
easier. If an equation has decimal numbers in it, we multiply each side of
the equation by a power of 10 large enough to eliminate any decimal
point. If the coefficient of x is not 1 (that is, a≠ 1 ) we might be able to
divide each side of the equation by this number to make the factoring
method or the quadratic formula easier. If the quadratic formula has frac-
tions in it, we can multiply both sides of the equation by the LCD to clear
the fraction(s), making the quadratic formula easier to use.
• Solve rational equations that lead to quadratic equations. Sometimes when
a rational equation is in the form “fraction = fraction,” we can cross-
multiply and be left with a quadratic equation. If the rational equation is
not in this form, then we multiply each term by the LCD and then solve
the quadratic equation. With either of these two methods, we could have
an extraneous solution, so we must make certain that the solution(s) do
not cause a 0 in a denominator in the original equation.