=-3x^2+12x-7

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Solution for =-3x^2+12x-7 equation:


Simplifying
0 = -3x2 + 12x + -7

Reorder the terms:
0 = -7 + 12x + -3x2

Solving
0 = -7 + 12x + -3x2

Solving for variable 'x'.

Combine like terms: 0 + 7 = 7
7 + -12x + 3x2 = -7 + 12x + -3x2 + 7 + -12x + 3x2

Reorder the terms:
7 + -12x + 3x2 = -7 + 7 + 12x + -12x + -3x2 + 3x2

Combine like terms: -7 + 7 = 0
7 + -12x + 3x2 = 0 + 12x + -12x + -3x2 + 3x2
7 + -12x + 3x2 = 12x + -12x + -3x2 + 3x2

Combine like terms: 12x + -12x = 0
7 + -12x + 3x2 = 0 + -3x2 + 3x2
7 + -12x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
7 + -12x + 3x2 = 0

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

Divide each side by '3'.
2.333333333 + -4x + x2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + -4x + -2.333333333 + x2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + -4x + x2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + -4x + x2 = 0 + -2.333333333
-4x + x2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
-4x + x2 = -2.333333333

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -2.333333333 + 4

Reorder the terms:
4 + -4x + x2 = -2.333333333 + 4

Combine like terms: -2.333333333 + 4 = 1.666666667
4 + -4x + x2 = 1.666666667

Factor a perfect square on the left side:
(x + -2)(x + -2) = 1.666666667

Calculate the square root of the right side: 1.290994449

Break this problem into two subproblems by setting 
(x + -2) equal to 1.290994449 and -1.290994449.

Subproblem 1

x + -2 = 1.290994449 Simplifying x + -2 = 1.290994449 Reorder the terms: -2 + x = 1.290994449 Solving -2 + x = 1.290994449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.290994449 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.290994449 + 2 x = 1.290994449 + 2 Combine like terms: 1.290994449 + 2 = 3.290994449 x = 3.290994449 Simplifying x = 3.290994449

Subproblem 2

x + -2 = -1.290994449 Simplifying x + -2 = -1.290994449 Reorder the terms: -2 + x = -1.290994449 Solving -2 + x = -1.290994449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.290994449 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.290994449 + 2 x = -1.290994449 + 2 Combine like terms: -1.290994449 + 2 = 0.709005551 x = 0.709005551 Simplifying x = 0.709005551

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.290994449, 0.709005551}

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