=12x^2-42x+5

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Solution for =12x^2-42x+5 equation:


Simplifying
0 = 12x2 + -42x + 5

Reorder the terms:
0 = 5 + -42x + 12x2

Solving
0 = 5 + -42x + 12x2

Solving for variable 'x'.

Combine like terms: 0 + -5 = -5
-5 + 42x + -12x2 = 5 + -42x + 12x2 + -5 + 42x + -12x2

Reorder the terms:
-5 + 42x + -12x2 = 5 + -5 + -42x + 42x + 12x2 + -12x2

Combine like terms: 5 + -5 = 0
-5 + 42x + -12x2 = 0 + -42x + 42x + 12x2 + -12x2
-5 + 42x + -12x2 = -42x + 42x + 12x2 + -12x2

Combine like terms: -42x + 42x = 0
-5 + 42x + -12x2 = 0 + 12x2 + -12x2
-5 + 42x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-5 + 42x + -12x2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
0.4166666667 + -3.5x + x2 = 0

Move the constant term to the right:

Add '-0.4166666667' to each side of the equation.
0.4166666667 + -3.5x + -0.4166666667 + x2 = 0 + -0.4166666667

Reorder the terms:
0.4166666667 + -0.4166666667 + -3.5x + x2 = 0 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + -3.5x + x2 = 0 + -0.4166666667
-3.5x + x2 = 0 + -0.4166666667

Combine like terms: 0 + -0.4166666667 = -0.4166666667
-3.5x + x2 = -0.4166666667

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = -0.4166666667 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = -0.4166666667 + 3.0625

Combine like terms: -0.4166666667 + 3.0625 = 2.6458333333
3.0625 + -3.5x + x2 = 2.6458333333

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 2.6458333333

Calculate the square root of the right side: 1.626601775

Break this problem into two subproblems by setting 
(x + -1.75) equal to 1.626601775 and -1.626601775.

Subproblem 1

x + -1.75 = 1.626601775 Simplifying x + -1.75 = 1.626601775 Reorder the terms: -1.75 + x = 1.626601775 Solving -1.75 + x = 1.626601775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 1.626601775 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 1.626601775 + 1.75 x = 1.626601775 + 1.75 Combine like terms: 1.626601775 + 1.75 = 3.376601775 x = 3.376601775 Simplifying x = 3.376601775

Subproblem 2

x + -1.75 = -1.626601775 Simplifying x + -1.75 = -1.626601775 Reorder the terms: -1.75 + x = -1.626601775 Solving -1.75 + x = -1.626601775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -1.626601775 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -1.626601775 + 1.75 x = -1.626601775 + 1.75 Combine like terms: -1.626601775 + 1.75 = 0.123398225 x = 0.123398225 Simplifying x = 0.123398225

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.376601775, 0.123398225}

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