9x-18=3x^2-12x+24

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Solution for 9x-18=3x^2-12x+24 equation:


Simplifying
9x + -18 = 3x2 + -12x + 24

Reorder the terms:
-18 + 9x = 3x2 + -12x + 24

Reorder the terms:
-18 + 9x = 24 + -12x + 3x2

Solving
-18 + 9x = 24 + -12x + 3x2

Solving for variable 'x'.

Reorder the terms:
-18 + -24 + 9x + 12x + -3x2 = 24 + -12x + 3x2 + -24 + 12x + -3x2

Combine like terms: -18 + -24 = -42
-42 + 9x + 12x + -3x2 = 24 + -12x + 3x2 + -24 + 12x + -3x2

Combine like terms: 9x + 12x = 21x
-42 + 21x + -3x2 = 24 + -12x + 3x2 + -24 + 12x + -3x2

Reorder the terms:
-42 + 21x + -3x2 = 24 + -24 + -12x + 12x + 3x2 + -3x2

Combine like terms: 24 + -24 = 0
-42 + 21x + -3x2 = 0 + -12x + 12x + 3x2 + -3x2
-42 + 21x + -3x2 = -12x + 12x + 3x2 + -3x2

Combine like terms: -12x + 12x = 0
-42 + 21x + -3x2 = 0 + 3x2 + -3x2
-42 + 21x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-42 + 21x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + 7x + -1x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-14 + 7x + -1x2)' equal to zero and attempt to solve: Simplifying -14 + 7x + -1x2 = 0 Solving -14 + 7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 14 + -7x + x2 = 0 Move the constant term to the right: Add '-14' to each side of the equation. 14 + -7x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + -7x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -7x + x2 = 0 + -14 -7x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 -7x + x2 = -14 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -14 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -14 + 12.25 Combine like terms: -14 + 12.25 = -1.75 12.25 + -7x + x2 = -1.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = -1.75 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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