-x^2-4x+1=0

Simple and best practice solution for -x^2-4x+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^2-4x+1=0 equation:


Simplifying
-1x2 + -4x + 1 = 0

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

Solving
1 + -4x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1 + 4x + x2 = 0

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 = 5
4 + 4x + x2 = 5

Factor a perfect square on the left side:
(x + 2)(x + 2) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + 2) equal to 2.236067978 and -2.236067978.

Subproblem 1

x + 2 = 2.236067978 Simplifying x + 2 = 2.236067978 Reorder the terms: 2 + x = 2.236067978 Solving 2 + x = 2.236067978 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 = 2.236067978 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.236067978 + -2 x = 2.236067978 + -2 Combine like terms: 2.236067978 + -2 = 0.236067978 x = 0.236067978 Simplifying x = 0.236067978

Subproblem 2

x + 2 = -2.236067978 Simplifying x + 2 = -2.236067978 Reorder the terms: 2 + x = -2.236067978 Solving 2 + x = -2.236067978 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 = -2.236067978 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.236067978 + -2 x = -2.236067978 + -2 Combine like terms: -2.236067978 + -2 = -4.236067978 x = -4.236067978 Simplifying x = -4.236067978

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.236067978, -4.236067978}

See similar equations:

| 10-8x=-3(4x+6) | | (7-z)(2z+5)=0 | | .18-(3x+5)=5(x-1)-6 | | 4x+14=90 | | f(x)=-x^2-4x+1 | | -3(x+7)=-4(x-1) | | 5r+34=8r+10 | | 3m-17=1 | | y=-7y+18 | | 29(f+7)-8=22 | | F+9=16 | | 2(z-6)=-4(z-9) | | (4x+3)=2x+10 | | 3m-17=18 | | 7.6x-2.1x=-99 | | 2*3a^2-5(3a)+6=0 | | 3x-3=12-6x-6x+3(2x+3) | | 3x*4x+4=125 | | 7=-10+y | | -4n+-1=-4n+-1 | | 3x+4=125 | | 3d+4=2d+6 | | 5x+12=2x+71 | | 3x-3=12-6x+3(2x+3) | | 4(x-3)=8(x+1) | | -4.9X^2+30.6X=0 | | 2r-4=2(6-7)r | | 9x+156=8x+168 | | 3(2x-4)=4(x+3) | | -2(t-7)+(t+5)=5 | | 2(3x+8)=10x+12 | | 4x+8x=-12 |

Equations solver categories