3x^2-24x+1=0

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Solution for 3x^2-24x+1=0 equation:


Simplifying
3x2 + -24x + 1 = 0

Reorder the terms:
1 + -24x + 3x2 = 0

Solving
1 + -24x + 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'.
0.3333333333 + -8x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -8x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -8x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -8x + x2 = 0 + -0.3333333333
-8x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-8x + x2 = -0.3333333333

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 = -0.3333333333 + 16

Reorder the terms:
16 + -8x + x2 = -0.3333333333 + 16

Combine like terms: -0.3333333333 + 16 = 15.6666666667
16 + -8x + x2 = 15.6666666667

Factor a perfect square on the left side:
(x + -4)(x + -4) = 15.6666666667

Calculate the square root of the right side: 3.958114029

Break this problem into two subproblems by setting 
(x + -4) equal to 3.958114029 and -3.958114029.

Subproblem 1

x + -4 = 3.958114029 Simplifying x + -4 = 3.958114029 Reorder the terms: -4 + x = 3.958114029 Solving -4 + x = 3.958114029 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 = 3.958114029 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.958114029 + 4 x = 3.958114029 + 4 Combine like terms: 3.958114029 + 4 = 7.958114029 x = 7.958114029 Simplifying x = 7.958114029

Subproblem 2

x + -4 = -3.958114029 Simplifying x + -4 = -3.958114029 Reorder the terms: -4 + x = -3.958114029 Solving -4 + x = -3.958114029 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 = -3.958114029 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.958114029 + 4 x = -3.958114029 + 4 Combine like terms: -3.958114029 + 4 = 0.041885971 x = 0.041885971 Simplifying x = 0.041885971

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.958114029, 0.041885971}

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