6x^2=6x-1

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


Simplifying
6x2 = 6x + -1

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

Solving
6x2 = -1 + 6x

Solving for variable 'x'.

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

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

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

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

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

Divide each side by '6'.
0.1666666667 + -1x + x2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -1x + -0.1666666667 + x2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + -1x + x2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + -1x + x2 = 0 + -0.1666666667
-1x + x2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
-1x + x2 = -0.1666666667

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -0.1666666667 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -0.1666666667 + 0.25

Combine like terms: -0.1666666667 + 0.25 = 0.0833333333
0.25 + -1x + x2 = 0.0833333333

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.0833333333

Calculate the square root of the right side: 0.288675135

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.288675135 and -0.288675135.

Subproblem 1

x + -0.5 = 0.288675135 Simplifying x + -0.5 = 0.288675135 Reorder the terms: -0.5 + x = 0.288675135 Solving -0.5 + x = 0.288675135 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.288675135 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.288675135 + 0.5 x = 0.288675135 + 0.5 Combine like terms: 0.288675135 + 0.5 = 0.788675135 x = 0.788675135 Simplifying x = 0.788675135

Subproblem 2

x + -0.5 = -0.288675135 Simplifying x + -0.5 = -0.288675135 Reorder the terms: -0.5 + x = -0.288675135 Solving -0.5 + x = -0.288675135 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.288675135 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.288675135 + 0.5 x = -0.288675135 + 0.5 Combine like terms: -0.288675135 + 0.5 = 0.211324865 x = 0.211324865 Simplifying x = 0.211324865

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.788675135, 0.211324865}

See similar equations:

| 4u-3=21 | | 10-1.5x+10=1.5x | | 4z^3+4z^2+8z= | | 8x-4(-x+9)=32 | | 10+v-9=20 | | (3s+5)(2s^2-8s+4)=0 | | -4x^2-2x=0 | | 2+4x-5=7x+7 | | -6y+4+12y=-6y+4(1+3y) | | 27x^2+324x=-72 | | 9-6=8-(9+a) | | 10-0.5(3x+20)=-1.5x | | 5(y+9)=3(y-4) | | 4z^3+4z^2+8z=0 | | 10x^4-50x^3+90x^2=0 | | 3w^2+9w= | | a^3+6a-11a= | | 3y+6y=2 | | (4x+2)(3x+4)=0 | | p^2-4= | | Y=0.5(6x+40) | | 5m*5m= | | F(-2)=3(-2)-2(-2)+5 | | x+20+x+8=180 | | n^2-4n+4=-2 | | 8x+5=19-6 | | 2a+3-99=3a+33 | | 21+.05=15+.11m | | X-8x-10=18 | | 9r^2-6r-35= | | 12x+5x+13x=180 | | n^2-4n+6=-2 |

Equations solver categories