-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
-1x2 + 6x = 1

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

Solving
6x + -1x2 = 1

Solving for variable 'x'.

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

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

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

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

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 = 8
9 + -6x + x2 = 8

Factor a perfect square on the left side:
(x + -3)(x + -3) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x + -3) equal to 2.828427125 and -2.828427125.

Subproblem 1

x + -3 = 2.828427125 Simplifying x + -3 = 2.828427125 Reorder the terms: -3 + x = 2.828427125 Solving -3 + x = 2.828427125 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 = 2.828427125 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.828427125 + 3 x = 2.828427125 + 3 Combine like terms: 2.828427125 + 3 = 5.828427125 x = 5.828427125 Simplifying x = 5.828427125

Subproblem 2

x + -3 = -2.828427125 Simplifying x + -3 = -2.828427125 Reorder the terms: -3 + x = -2.828427125 Solving -3 + x = -2.828427125 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 = -2.828427125 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.828427125 + 3 x = -2.828427125 + 3 Combine like terms: -2.828427125 + 3 = 0.171572875 x = 0.171572875 Simplifying x = 0.171572875

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.828427125, 0.171572875}

See similar equations:

| x/11=11/36x | | W-3/4=-7/8 | | 8(2n+4)=9(9n+7)+2 | | X-2*-2+2=0 | | X-(2x-2)+2=0 | | 4c-9=c+9 | | 7*x/3=28 | | -0.88888888888889x+0.33333333333333=0.22222222222222 | | 12w-5=-35w-10 | | x^2(y+1)=9(y+1)+4x+12 | | 12x-5x-59=116 | | -100+9x+4x=147 | | -122-3x+10x=81 | | -32-x+5x=28 | | -7x+12x-61=39 | | x-7.3/4.5=2.4 | | 8-(6-9)=5 | | 7x-6x-8=16 | | 7x-6z-8=16 | | 11.57=x=22.74/0.7 | | 6(6/4)6 | | -4x-39+8x=61 | | 12x-8x-89=27 | | -1-6z+1=2 | | (n+1)(7n-8)=0 | | 5x-27-2x=39 | | 6x-(5x+3)=2x-23 | | 3(2x-1)=-2(4x+3) | | -17+3(0.25)=x | | 5x-3x-20=26 | | 5.21-10.9x=9.57 | | 8x-45-5x=42 |

Equations solver categories