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x^(2) - 2x - 3 = 0
This is a Quadratic Equation.
There are three methods to solve.
#1 ; Factor
#2 ; Complete the Square
#3 ; Use the Quadratic Equation.
Use #1 , which is the simplest method.
We note that 'x^(2) ' has a coefficient of '1' (not Shown).
We also note that the constant is '-3' . So write down the factors of '3', which are 1, & .3.
From '1' & '3' we add/subtract to make '2' the coefficient of the middle term. Hence 1 - 3 = -2
Writing up our brackets
( x 1)(x 3) = 0
Since the sign of the constant '3' is negative (-), it means that the two signs in the brackets are different (+/-)
Since the '2' is negative, then the larger number in the brackets is the negative term.
Hence
( x + 1)(x - 3) = 0
Equating each bracket to zero.
x + 1 = 0 Hence x = -1
&
x - 3 = 0 Hence x = 3
So the two solutions for 'x' are '-1' & '3'.
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