Question

G(x) = x² + 4x-1
Solve

Answer 1

x = - 2 ±
`√(5)`

Explanation:

Given

g(x) = x² + 4x - 1

To solve for x let g(x) = 0, that is

x² + 4x - 1 = 0 ( add 1 to both sides )

x² + 4x = 1

Using the method of completing the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(2)x + 4 = 1 + 4

(x + 2)² = 5 ( take the square root of both sides )

x + 2 = ±
`√(5)` ( subtract 2 from both sides )

x = - 2 ±
`√(5)`

Thus solutions in exact form are

x = - 2 -
`√(5)` , x = - 2 +
`√(5)`

Answer 2

Using the quadratic formula:

x = [-4 +- sqr root (16 - 4 * 1 * -1)] / 2 *1

x = [-4 +- sqr root (20)] / 2

x1 = [-4 + sqr root (20)] / 2

x2 = [-4 - sqr root (20)] / 2

x1 = 0.23607

x2 = -4.2361

Explanation: