77-72x+12x^2=0

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Solution for 77-72x+12x^2=0 equation:


Simplifying
77 + -72x + 12x2 = 0

Solving
77 + -72x + 12x2 = 0

Solving for variable 'x'.

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

Divide each side by '12'.
6.416666667 + -6x + x2 = 0

Move the constant term to the right:

Add '-6.416666667' to each side of the equation.
6.416666667 + -6x + -6.416666667 + x2 = 0 + -6.416666667

Reorder the terms:
6.416666667 + -6.416666667 + -6x + x2 = 0 + -6.416666667

Combine like terms: 6.416666667 + -6.416666667 = 0.000000000
0.000000000 + -6x + x2 = 0 + -6.416666667
-6x + x2 = 0 + -6.416666667

Combine like terms: 0 + -6.416666667 = -6.416666667
-6x + x2 = -6.416666667

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 = -6.416666667 + 9

Reorder the terms:
9 + -6x + x2 = -6.416666667 + 9

Combine like terms: -6.416666667 + 9 = 2.583333333
9 + -6x + x2 = 2.583333333

Factor a perfect square on the left side:
(x + -3)(x + -3) = 2.583333333

Calculate the square root of the right side: 1.607275127

Break this problem into two subproblems by setting 
(x + -3) equal to 1.607275127 and -1.607275127.

Subproblem 1

x + -3 = 1.607275127 Simplifying x + -3 = 1.607275127 Reorder the terms: -3 + x = 1.607275127 Solving -3 + x = 1.607275127 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 = 1.607275127 + 3 Combine like terms: -3 + 3 = 0 0 + x = 1.607275127 + 3 x = 1.607275127 + 3 Combine like terms: 1.607275127 + 3 = 4.607275127 x = 4.607275127 Simplifying x = 4.607275127

Subproblem 2

x + -3 = -1.607275127 Simplifying x + -3 = -1.607275127 Reorder the terms: -3 + x = -1.607275127 Solving -3 + x = -1.607275127 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 = -1.607275127 + 3 Combine like terms: -3 + 3 = 0 0 + x = -1.607275127 + 3 x = -1.607275127 + 3 Combine like terms: -1.607275127 + 3 = 1.392724873 x = 1.392724873 Simplifying x = 1.392724873

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.607275127, 1.392724873}

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