Question

How do I solve this?

Answer 1

first option

Explanation:

to find the zeros equate f(x) to zero , that is

2x² + 8x - 3 = 0 ( add 3 to both sides )

2x² + 8x = 3 ← factor out 2 from each term on the left side

2(x² + 4x) = 3

to complete the square

add/subtract ( half the coefficient of the x- term )² to x² + 4x

2(x² + 2(2)x + 4 - 4) = 3

2(x + 2)² - 8 = 3 ( add 8 to both sides )

2(x + 2)² = 11 ( divide both sides by 2 )

(x + 2)² =
`(11)/(2)` ( take square root of both sides )

x + 2 = ±
`\sqrt{(11)/(2) }` ( subtract 2 from both sides )

x = - 2 ±
`\sqrt{(11)/(2) }`

that is

x = - 2 -
`\sqrt{(11)/(2) }` , x = - 2 +
`\sqrt{(11)/(2) }`

Answer 2

x = -2 - √11/2 and - 2 + √11/2.

Explanation:

2x^2 + 8x - 3 = 0

Divide first 2 terms by 2:

2(x^2 + 4x) - 3 = 0

2(x^2 + 4x) = 3

Complete the square:

2 [ (x + 2)^2 - 2^2) = 3

2(x + 2)^2 - 8 = 3

2(x + 2)^2 = 11

(x + 2)*2 = 11/2

x + 2 = ± 11/2

x = -2 ± √11/2