Where should the parentheses go in this equation 1+2·3+4·5=65
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x = 5 or x = -
simplify the left side by combining the fractions
-
=
= =
=
( cross- multiply )
24x = 5 (x² - 1)
24x = 5x² - 5 ( rearrange into standard form )
5x² - 24x - 5 = 0 ← in standard form
consider the factors of the product 5 × - 5 = - 25 which sum to - 24
The factors are - 25 and + 1 ( split the middle term using these factors )
5x² - 25x + x - 5 = 0 ( factor by grouping )
5x( x - 5 ) + 1( x - 5 ) = 0 ( take out common factor (x - 5 ) )
(x - 5 )( 5x + 1 ) = 0
equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
5x + 1 = 0 ⇒ x = -