3x^2-68x+12=0

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Solution for 3x^2-68x+12=0 equation:


Simplifying
3x2 + -68x + 12 = 0

Reorder the terms:
12 + -68x + 3x2 = 0

Solving
12 + -68x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
4 + -22.66666667x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -22.66666667x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -22.66666667x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -22.66666667x + x2 = 0 + -4
-22.66666667x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-22.66666667x + x2 = -4

The x term is -22.66666667x.  Take half its coefficient (-11.33333334).
Square it (128.4444446) and add it to both sides.

Add '128.4444446' to each side of the equation.
-22.66666667x + 128.4444446 + x2 = -4 + 128.4444446

Reorder the terms:
128.4444446 + -22.66666667x + x2 = -4 + 128.4444446

Combine like terms: -4 + 128.4444446 = 124.4444446
128.4444446 + -22.66666667x + x2 = 124.4444446

Factor a perfect square on the left side:
(x + -11.33333334)(x + -11.33333334) = 124.4444446

Calculate the square root of the right side: 11.155467027

Break this problem into two subproblems by setting 
(x + -11.33333334) equal to 11.155467027 and -11.155467027.

Subproblem 1

x + -11.33333334 = 11.155467027 Simplifying x + -11.33333334 = 11.155467027 Reorder the terms: -11.33333334 + x = 11.155467027 Solving -11.33333334 + x = 11.155467027 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.33333334' to each side of the equation. -11.33333334 + 11.33333334 + x = 11.155467027 + 11.33333334 Combine like terms: -11.33333334 + 11.33333334 = 0.00000000 0.00000000 + x = 11.155467027 + 11.33333334 x = 11.155467027 + 11.33333334 Combine like terms: 11.155467027 + 11.33333334 = 22.488800367 x = 22.488800367 Simplifying x = 22.488800367

Subproblem 2

x + -11.33333334 = -11.155467027 Simplifying x + -11.33333334 = -11.155467027 Reorder the terms: -11.33333334 + x = -11.155467027 Solving -11.33333334 + x = -11.155467027 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.33333334' to each side of the equation. -11.33333334 + 11.33333334 + x = -11.155467027 + 11.33333334 Combine like terms: -11.33333334 + 11.33333334 = 0.00000000 0.00000000 + x = -11.155467027 + 11.33333334 x = -11.155467027 + 11.33333334 Combine like terms: -11.155467027 + 11.33333334 = 0.177866313 x = 0.177866313 Simplifying x = 0.177866313

Solution

The solution to the problem is based on the solutions from the subproblems. x = {22.488800367, 0.177866313}

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