Solve for X; X^2 + 4X = 1?

Question

Solve by factoring or quadratic formula... I can't use decimals. Improper fractions are fine.

can you solve this by taking the square root or factoring only?

Answer 1

Completing the square

x² + 4x = 1

x² + 4x +______ = 1 +_____

x² + 4x + 4 = 1 + 4

(x + 2)(x + 2) = 5

(x + 2)² = 5

(√x + 2)² = ± √5

x + 2 = ± 2.236067978

x + 2 - 2 = - 2 ± 2.236067978

x = - 2 ± 2.236067978

- - - - - - - -

Solving for +

x = - 2 + 2.236067978

x = 0.236067978

- - - - - - - - - - -

Solving for -

x = - 2 - 2.236067978

x = - 4.236067978

- - - - - - - - - -s-

Answer 2

using the quadratic equations formula
ie. x= (-b +( b^2 - 4ac)^1/2)/2a and (-b -( b^2 - 4ac)^1/2)/2a
where equation is ax^2 +bx +c =0
thus as equation is

x^2 +4x -1 =0
x= (-4 + ( 16 + 4 )^1/2 )/2 or (-4 - ( 16 + 4 )^1/2 )/2
= ( -4 + 20^1/2 )/2 or ( -4 -20^1/2)/2
= (-2 + 5^1/2) or (-4 - 5^1/2)
x = 4.236 or -0.236

Answer 3

x^2 +4x =1
add +4 to both sides
x^2 +4x +4 =1+4
x^2 +4x +4 =5
take square root of both sides
(x+2) = + (square root of )5 (x +2) = - (sqare root of) 5
x= -2 +square root of 5 x= -2 -square root of 5

Answer 4

x^2+4x=1
x^2+4x+1=0
(x+3)(x-4)=0
x=-3 or x=4
when you take a number to the other side of the = sign it changes its sign (+ or -) to the opposite of what is was.

Answer 5

quadratic formula:
Generally

ax^2 +bx +c = 0

D = b^2 - 4ac

x1 = (-b + sqrtD)/2a
x2 = (-b - sqrtD)/2a

Here X^2 + 4X = 1 => X^2 + 4X - 1 = 0

D = 16 + 4 = 20

x1,2 = (-4 +/- sqrt20)/2

Answer 6

x^2+4x=1

x^2+4x-1=0



using quadratic
equation:
-4+-sqrt(4^2-4(-1)(1))/2=
-4.23606797749979
0.23606797749979

Answer 7

x^2 + 4x = 1
x^2 + 4x - 1 = 0

x = [-4 +/- sqrt(16 - 4(-1))] / 2
x = [-4 +/- sqrt(16 + 4)] / 2
x = [-4 +/- sqrt(20)] / 2
x = [-4 +/- sqrt(4*5)] / 2
x = [-4 +/- 2sqrt(5)] / 2
x = -2 +/- sqrt(5)

Answer 8

heres your homework:
X^2+4X-1=0

(x+3) (x-4)

X= -3 OR +4

factoring

Answer 9

If x=(-b+(b^2-4ac)^1/2)/(2a)
Then x=(-4+(4^2+4)^1/2)/2
x=(-4+(20)^1/2)/2
x=(-4+2*5^1/2)/2
x=(2*(-2+5^1/2))/2
x=-2+5^1/2

and also remember that
If x=(-b-(b^2-4ac)^1/2)/(2a)
Then x=(-4-(4^2+4)^1/2)/2
x=(-4-(20)^1/2)/2
x=(-4-2*5^1/2)/2
x=(2*(-2-5^1/2))/2
x=-2-5^1/2