9x^2=18x-84

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Solution for 9x^2=18x-84 equation: 


Simplifying
9x2 = 18x + -84

Reorder the terms:
9x2 = -84 + 18x

Solving
9x2 = -84 + 18x

Solving for variable 'x'.

Reorder the terms:
84 + -18x + 9x2 = -84 + 18x + 84 + -18x

Reorder the terms:
84 + -18x + 9x2 = -84 + 84 + 18x + -18x

Combine like terms: -84 + 84 = 0
84 + -18x + 9x2 = 0 + 18x + -18x
84 + -18x + 9x2 = 18x + -18x

Combine like terms: 18x + -18x = 0
84 + -18x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(28 + -6x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(28 + -6x + 3x2)' equal to zero and attempt to solve:

Simplifying
28 + -6x + 3x2 = 0

Solving
28 + -6x + 3x2 = 0

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

Divide each side by '3'.
9.333333333 + -2x + x2 = 0

Move the constant term to the right:

Add '-9.333333333' to each side of the equation.
9.333333333 + -2x + -9.333333333 + x2 = 0 + -9.333333333

Reorder the terms:
9.333333333 + -9.333333333 + -2x + x2 = 0 + -9.333333333

Combine like terms: 9.333333333 + -9.333333333 = 0.000000000
0.000000000 + -2x + x2 = 0 + -9.333333333
-2x + x2 = 0 + -9.333333333

Combine like terms: 0 + -9.333333333 = -9.333333333
-2x + x2 = -9.333333333

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -9.333333333 + 1

Reorder the terms:
1 + -2x + x2 = -9.333333333 + 1

Combine like terms: -9.333333333 + 1 = -8.333333333
1 + -2x + x2 = -8.333333333

Factor a perfect square on the left side:
(x + -1)(x + -1) = -8.333333333

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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