Question

Itranscript Solve the following equation. 60x^(2)+3x-3=0

Answer 1

x = -
`(1)/(4)` , x =
`(1)/(5)`

Explanation:

60x² + 3x - 3 = 0 ( divide through by 3 )

20x² + x - 1 = 0 ← in standard form

consider the factors of the product of the constant term and the coefficient of the x² term which sum to give the coefficient of the x- term.

product = 20 × - 1 = - 20 and sum = + 1

the factors are + 5 and - 4

use these factors to split the x- term

20x² + 5x - 4x - 1 = 0 ( factor the first/second and third/fourth terms )

5x(4x + 1) - 1(4x + 1) = 0 ← factor out ( 4x + 1 ) from each term

(4x + 1)(5x - 1) = 0 ← in factored form

equate each factor to zero and solve for x

4x + 1 = 0 ( subtract 1 from both sides )

4x = - 1 ( divide both sides by 4 )

x = -
`(1)/(4)`

5x - 1 = 0 ( add 1 to both sides )

5x = 1 ( divide both sides by 5 )

x =
`(1)/(5)`

solutions are x = -
`(1)/(4)` , x =
`(1)/(5)`