12x^2-96x+143=0

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Solution for 12x^2-96x+143=0 equation:


Simplifying
12x2 + -96x + 143 = 0

Reorder the terms:
143 + -96x + 12x2 = 0

Solving
143 + -96x + 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'.
11.91666667 + -8x + x2 = 0

Move the constant term to the right:

Add '-11.91666667' to each side of the equation.
11.91666667 + -8x + -11.91666667 + x2 = 0 + -11.91666667

Reorder the terms:
11.91666667 + -11.91666667 + -8x + x2 = 0 + -11.91666667

Combine like terms: 11.91666667 + -11.91666667 = 0.00000000
0.00000000 + -8x + x2 = 0 + -11.91666667
-8x + x2 = 0 + -11.91666667

Combine like terms: 0 + -11.91666667 = -11.91666667
-8x + x2 = -11.91666667

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -11.91666667 + 16

Reorder the terms:
16 + -8x + x2 = -11.91666667 + 16

Combine like terms: -11.91666667 + 16 = 4.08333333
16 + -8x + x2 = 4.08333333

Factor a perfect square on the left side:
(x + -4)(x + -4) = 4.08333333

Calculate the square root of the right side: 2.020725941

Break this problem into two subproblems by setting 
(x + -4) equal to 2.020725941 and -2.020725941.

Subproblem 1

x + -4 = 2.020725941 Simplifying x + -4 = 2.020725941 Reorder the terms: -4 + x = 2.020725941 Solving -4 + x = 2.020725941 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 2.020725941 + 4 Combine like terms: -4 + 4 = 0 0 + x = 2.020725941 + 4 x = 2.020725941 + 4 Combine like terms: 2.020725941 + 4 = 6.020725941 x = 6.020725941 Simplifying x = 6.020725941

Subproblem 2

x + -4 = -2.020725941 Simplifying x + -4 = -2.020725941 Reorder the terms: -4 + x = -2.020725941 Solving -4 + x = -2.020725941 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -2.020725941 + 4 Combine like terms: -4 + 4 = 0 0 + x = -2.020725941 + 4 x = -2.020725941 + 4 Combine like terms: -2.020725941 + 4 = 1.979274059 x = 1.979274059 Simplifying x = 1.979274059

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.020725941, 1.979274059}

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