x^2-6x=6

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


Simplifying
x2 + -6x = 6

Reorder the terms:
-6x + x2 = 6

Solving
-6x + x2 = 6

Solving for variable 'x'.

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 6 + 9

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

Combine like terms: 6 + 9 = 15
9 + -6x + x2 = 15

Factor a perfect square on the left side:
(x + -3)(x + -3) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(x + -3) equal to 3.872983346 and -3.872983346.

Subproblem 1

x + -3 = 3.872983346 Simplifying x + -3 = 3.872983346 Reorder the terms: -3 + x = 3.872983346 Solving -3 + x = 3.872983346 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 = 3.872983346 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.872983346 + 3 x = 3.872983346 + 3 Combine like terms: 3.872983346 + 3 = 6.872983346 x = 6.872983346 Simplifying x = 6.872983346

Subproblem 2

x + -3 = -3.872983346 Simplifying x + -3 = -3.872983346 Reorder the terms: -3 + x = -3.872983346 Solving -3 + x = -3.872983346 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 = -3.872983346 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.872983346 + 3 x = -3.872983346 + 3 Combine like terms: -3.872983346 + 3 = -0.872983346 x = -0.872983346 Simplifying x = -0.872983346

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.872983346, -0.872983346}

See similar equations:

| 2x+y=-8 | | 5x^2+8x-6=0 | | -8=2*0 | | 15(t-2)+3=6(3t+4)-10 | | X^2+Y^2-3X-4Y+4=0 | | 12x=8400 | | 2(X-4)+2Y^2=18 | | 6x-12=36-10x | | 16n+192=4n | | 4=-y+3 | | 4*-1=-y+3 | | 6p-8=10 | | 9y+108=45y | | 15x-9x+12=6 | | 15x-9x+11=6 | | 2(6z-1)-5(z+4)=2(z+1) | | 8x-32=28 | | 0=-y+2 | | 4*-1=-y+2 | | 2x-8=8x+4 | | 2*-1=-y+2 | | 7x-12=x+6(2+x) | | .75w+8=.33w-7 | | 7xy^2-5xy(2-y)= | | -7=4(x+3)+5x | | .5w+7=2w-2 | | -4n+10+2n=18 | | 7xy-5xy(2-y)= | | -(5y+5)-(4y-7)=1 | | w-2d=4 | | =-1 | | 6(1-t)-(2-4t)=1 |

Equations solver categories