x^2+6x=1

Simple and best practice solution for x^2+6x=1 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+6x=1 equation:


Simplifying
x2 + 6x = 1

Reorder the terms:
6x + x2 = 1

Solving
6x + x2 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + 6x + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 6x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 6x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 6x + x2 = 0 + 1
6x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
6x + x2 = 1

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 1 + 9

Reorder the terms:
9 + 6x + x2 = 1 + 9

Combine like terms: 1 + 9 = 10
9 + 6x + x2 = 10

Factor a perfect square on the left side:
(x + 3)(x + 3) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + 3) equal to 3.16227766 and -3.16227766.

Subproblem 1

x + 3 = 3.16227766 Simplifying x + 3 = 3.16227766 Reorder the terms: 3 + x = 3.16227766 Solving 3 + x = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.16227766 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.16227766 + -3 x = 3.16227766 + -3 Combine like terms: 3.16227766 + -3 = 0.16227766 x = 0.16227766 Simplifying x = 0.16227766

Subproblem 2

x + 3 = -3.16227766 Simplifying x + 3 = -3.16227766 Reorder the terms: 3 + x = -3.16227766 Solving 3 + x = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.16227766 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.16227766 + -3 x = -3.16227766 + -3 Combine like terms: -3.16227766 + -3 = -6.16227766 x = -6.16227766 Simplifying x = -6.16227766

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.16227766, -6.16227766}

See similar equations:

| (a+4)(a-2)= | | 6x-7y=14 | | x-6y=30 | | 3x(x-1)=2(x^2+27) | | 2x+5y=19 | | 4+9n-3n^2=2-n | | 7x+4=2x+5 | | 4x^2+4x+12= | | 6x+3x^2+12= | | 4(x-1)=2(3x-1)+(1-2x) | | 82-4t=22+2t | | 9(t+4)-29=25 | | x^4+5x^3+5x^2-5x-6=0 | | 20+6x=7x+4(3x-8) | | 8(3x+6)=36 | | 9x^3=12x^4 | | 9x^2=12x^4 | | 2z-27=11 | | 55y-5y=200 | | 3x^2+7x-24=13x | | m^2+5m-99=3m | | (x-2)(x+7)=0 | | -3x^2+75=0 | | 4(2x-3)+5(2x-3)=3(2x-3) | | x^2-6x=40 | | -9x+15=-22+-4(x+12) | | 9x^3-144= | | x^2-9x=0 | | 5x+-8=13+7(x-3) | | x^2-11x+18=0 | | (4x+7)(7x-9)=0 | | 14+-9x=-8(10+x) |

Equations solver categories