Question

I need help for my homework

Answer 1

x = 1 and x = -5/2

Explanation:

Given the form ax²+bx+c = 0, and a≠1, it's easiest to split the "b" term and factor by parts:

1. Identify a=2, b=3, and c= -5

2. Multiply ac = 2(-5) = -10

3. Find Factors of -10 (ac) that add to +3 (b): +5, -2

4. Rewrite equation with the new "middle" terms:

2x² -2x +5x -5 = 0

5. Split the left side into two binomials and factor out the GCF from each:

2x² -2x = 2x(x-1) and 5x -5 = 5(x-1)

6. Notice the (x-1) in both cases!! This is one of your factors. :) The other factor is the combined GCFs from each case: (x -1)(2x +5) = 0

7. Set each factor =0 and solve:

x - 1 = 0 ==> x = 1 and 2x +5 = 0 ==> x = -5/2

Answer 2

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

Explanation:

2x² + 3x - 5 = 0

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 = + 3

the factors are - 2 and + 5

use these factors to split the x- term

2x² - 2x + 5x - 5 = 0 ( factor 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

2x + 5 = 0 ( subtract 5 from both sides )

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

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

and

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

x = 1