Not all quadratic expressions will be as easy to factor as the previous examples and problems were. Sometimes you will need to multiply or divide both sides of the equation by a number. Because zero multiplied or divided by any nonzero number is still zero, only one side of the equation will change. Keep in mind that not all quadratic expressions can be factored using rational numbers (fractions) or even real numbers. Fortunately there
is another
way of solving quadratic equations, which bypasses the factoring method.
Examples
The equation
_x2 + 4x – 3 = 0 is awkward to factor because of the negative sign
in front of x2. Multiply both sides of the equation by –1 then
factor.
Decimals and
fractions in a quadratic equation can be eliminated in the same way. Multiply
both sides of the equation by a power of 10 to eliminate decimal points.
Multiply both sides of the equation by the LCD to eliminate fractions.
0.1x2 – 1.5x + 5.6 = 0
Multiply
both sides of the equation by 10 to clear the decimal.
Clear the
fraction by multiplying both sides of the equation by 4 (the LCD).
Practice
Solutions
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