6((x-3)(x-3))+4=0

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Solution for 6((x-3)(x-3))+4=0 equation:


Simplifying
6((x + -3)(x + -3)) + 4 = 0

Reorder the terms:
6((-3 + x)(x + -3)) + 4 = 0

Reorder the terms:
6((-3 + x)(-3 + x)) + 4 = 0

Multiply (-3 + x) * (-3 + x)
6((-3(-3 + x) + x(-3 + x))) + 4 = 0
6(((-3 * -3 + x * -3) + x(-3 + x))) + 4 = 0
6(((9 + -3x) + x(-3 + x))) + 4 = 0
6((9 + -3x + (-3 * x + x * x))) + 4 = 0
6((9 + -3x + (-3x + x2))) + 4 = 0

Combine like terms: -3x + -3x = -6x
6((9 + -6x + x2)) + 4 = 0
(9 * 6 + -6x * 6 + x2 * 6) + 4 = 0
(54 + -36x + 6x2) + 4 = 0

Reorder the terms:
54 + 4 + -36x + 6x2 = 0

Combine like terms: 54 + 4 = 58
58 + -36x + 6x2 = 0

Solving
58 + -36x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(29 + -18x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(29 + -18x + 3x2)' equal to zero and attempt to solve:

Simplifying
29 + -18x + 3x2 = 0

Solving
29 + -18x + 3x2 = 0

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

Divide each side by '3'.
9.666666667 + -6x + x2 = 0

Move the constant term to the right:

Add '-9.666666667' to each side of the equation.
9.666666667 + -6x + -9.666666667 + x2 = 0 + -9.666666667

Reorder the terms:
9.666666667 + -9.666666667 + -6x + x2 = 0 + -9.666666667

Combine like terms: 9.666666667 + -9.666666667 = 0.000000000
0.000000000 + -6x + x2 = 0 + -9.666666667
-6x + x2 = 0 + -9.666666667

Combine like terms: 0 + -9.666666667 = -9.666666667
-6x + x2 = -9.666666667

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 = -9.666666667 + 9

Reorder the terms:
9 + -6x + x2 = -9.666666667 + 9

Combine like terms: -9.666666667 + 9 = -0.666666667
9 + -6x + x2 = -0.666666667

Factor a perfect square on the left side:
(x + -3)(x + -3) = -0.666666667

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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