Question

PLEASE HELP
Solve for x.

X^2+4x+4=18

Answer 1

x = -2 ± 3√2

Explanation:

x^2 + 4x + 4 = 18:

or, (x + 2)^2 = 18

Taking the square root of both sides, we get:

or, x + 2 = ±√18

or, x + 2 = ±3√2

or,x = -2 ± 3√2

therefore, x = -2 + 3√2 or x = -2 - 3√2

or,

using Shridharacharya's formula

x = (-b ± √(b^2 - 4ac)) / (2a)

now,

x^2 + 4x + 4 = 18.

or, x^2 + 4x + 4 - 18 = 0

or, x^2 + 4x - 14 = 0

or, x = (-4 ± √(4^2 - 4(1)(-14))) / (2(1))

or, x = (-4 ± √(16 + 56)) / 2

or, x = (-4 ± √72) / 2

(√72 = √(36 x 2) =6√2)

or, x = (-4 ±6√2 ) / 2

or, x = -2 ± 3√2

Therefore,x = -2 + 3√2 and x = -2 - 3√2.