Question

Solve 2x²+7x+5=0 using factorisation method

Answer 1

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

Explanation:

given the equation

2x² + 7x + 5 = 0 ← quadratic equation in standard form

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

product = 2 × 5 = 10 and sum = + 7

the factors are + 2 and + 5

use these factors to split the x- term

2x² + 2x + 5x + 5 = 0 ( factor the first/second and third/fourth terms )

2x(x + 1) + 5(x + 1) = 0 ← factor out (x + 1) from each term

(x + 1)(2x + 5) = 0 ← in factored form

equate each factor to zero and solve for x

x + 1 = 0 ( subtract 1 from each side )

x = - 1

2x + 5 = 0 ( subtract 5 from each term )

2x = - 5 ( divide both sides by 2 )

x = -
`(5)/(2)`

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