# 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 1x + -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 2x + -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

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