x^2+4*x+1=0

Simple and best practice solution for x^2+4*x+1=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for x^2+4*x+1=0 equation:


Simplifying
x2 + 4x + 1 = 0

Reorder the terms:
1 + 4x + x2 = 0

Solving
1 + 4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 4x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 4x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4x + x2 = 0 + -1
4x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
4x + x2 = -1

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = -1 + 4

Reorder the terms:
4 + 4x + x2 = -1 + 4

Combine like terms: -1 + 4 = 3
4 + 4x + x2 = 3

Factor a perfect square on the left side:
(x + 2)(x + 2) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + 2) equal to 1.732050808 and -1.732050808.

Subproblem 1

x + 2 = 1.732050808 Simplifying x + 2 = 1.732050808 Reorder the terms: 2 + x = 1.732050808 Solving 2 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.732050808 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.732050808 + -2 x = 1.732050808 + -2 Combine like terms: 1.732050808 + -2 = -0.267949192 x = -0.267949192 Simplifying x = -0.267949192

Subproblem 2

x + 2 = -1.732050808 Simplifying x + 2 = -1.732050808 Reorder the terms: 2 + x = -1.732050808 Solving 2 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.732050808 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.732050808 + -2 x = -1.732050808 + -2 Combine like terms: -1.732050808 + -2 = -3.732050808 x = -3.732050808 Simplifying x = -3.732050808

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.267949192, -3.732050808}

See similar equations:

| -4=2-6h | | 6x-8=122 | | 52-7x=3 | | -1/4a-4=7/4-3 | | 2d+9=31 | | f(4x)=4f(x) | | x=sqrt(x+7+5) | | 5(u-3)-9=-5(-6u+2)-9u | | 7x^2-47+30=0 | | 9z=13-49 | | 4=1/4w=6 | | 15w-17w=12 | | 3x+4(2x-5)=-4-5x | | x=-2x/5 | | 0=5x^2+2x+6 | | 2x^2+16=9 | | (4-x)(2x-8x)= | | 4x^2+20-48=0 | | 6x-3-5/4=3-x/5 | | 3x/2=20-5x | | s=2wrh | | x^2-16+9=0 | | 4x^2+4x+2=86 | | q+-37=-15 | | h(x)=3x-3 | | r-76=-16 | | -8=s/3 | | -8=s/6 | | -5=s/-5 | | -7c=91 | | 63=t+-33 | | -9(x+2)-2=-20 |

Equations solver categories