(6x)(6x)-84x+510=0

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Solution for (6x)(6x)-84x+510=0 equation:


Simplifying
(6x)(6x) + -84x + 510 = 0

Remove parenthesis around (6x)
6x(6x) + -84x + 510 = 0

Remove parenthesis around (6x)
6x * 6x + -84x + 510 = 0

Reorder the terms for easier multiplication:
6 * 6x * x + -84x + 510 = 0

Multiply 6 * 6
36x * x + -84x + 510 = 0

Multiply x * x
36x2 + -84x + 510 = 0

Reorder the terms:
510 + -84x + 36x2 = 0

Solving
510 + -84x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(85 + -14x + 6x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(85 + -14x + 6x2)' equal to zero and attempt to solve:

Simplifying
85 + -14x + 6x2 = 0

Solving
85 + -14x + 6x2 = 0

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

Divide each side by '6'.
14.16666667 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '-14.16666667' to each side of the equation.
14.16666667 + -2.333333333x + -14.16666667 + x2 = 0 + -14.16666667

Reorder the terms:
14.16666667 + -14.16666667 + -2.333333333x + x2 = 0 + -14.16666667

Combine like terms: 14.16666667 + -14.16666667 = 0.00000000
0.00000000 + -2.333333333x + x2 = 0 + -14.16666667
-2.333333333x + x2 = 0 + -14.16666667

Combine like terms: 0 + -14.16666667 = -14.16666667
-2.333333333x + x2 = -14.16666667

The x term is -2.333333333x.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333x + 1.361111112 + x2 = -14.16666667 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = -14.16666667 + 1.361111112

Combine like terms: -14.16666667 + 1.361111112 = -12.805555558
1.361111112 + -2.333333333x + x2 = -12.805555558

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = -12.805555558

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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