-3*X*X+6X=-1

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Solution for -3*X*X+6X=-1 equation:


Simplifying
-3X * X + 6X = -1

Multiply X * X
-3X2 + 6X = -1

Reorder the terms:
6X + -3X2 = -1

Solving
6X + -3X2 = -1

Solving for variable 'X'.

Reorder the terms:
1 + 6X + -3X2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + 6X + -3X2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-0.3333333333 + -2X + X2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + -2X + 0.3333333333 + X2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + -2X + X2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + -2X + X2 = 0 + 0.3333333333
-2X + X2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
-2X + X2 = 0.3333333333

The X term is -2X.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2X + 1 + X2 = 0.3333333333 + 1

Reorder the terms:
1 + -2X + X2 = 0.3333333333 + 1

Combine like terms: 0.3333333333 + 1 = 1.3333333333
1 + -2X + X2 = 1.3333333333

Factor a perfect square on the left side:
(X + -1)(X + -1) = 1.3333333333

Calculate the square root of the right side: 1.154700538

Break this problem into two subproblems by setting 
(X + -1) equal to 1.154700538 and -1.154700538.

Subproblem 1

X + -1 = 1.154700538 Simplifying X + -1 = 1.154700538 Reorder the terms: -1 + X = 1.154700538 Solving -1 + X = 1.154700538 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + X = 1.154700538 + 1 Combine like terms: -1 + 1 = 0 0 + X = 1.154700538 + 1 X = 1.154700538 + 1 Combine like terms: 1.154700538 + 1 = 2.154700538 X = 2.154700538 Simplifying X = 2.154700538

Subproblem 2

X + -1 = -1.154700538 Simplifying X + -1 = -1.154700538 Reorder the terms: -1 + X = -1.154700538 Solving -1 + X = -1.154700538 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + X = -1.154700538 + 1 Combine like terms: -1 + 1 = 0 0 + X = -1.154700538 + 1 X = -1.154700538 + 1 Combine like terms: -1.154700538 + 1 = -0.154700538 X = -0.154700538 Simplifying X = -0.154700538

Solution

The solution to the problem is based on the solutions from the subproblems. X = {2.154700538, -0.154700538}

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