-6x=3x^2+9

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Solution for -6x=3x^2+9 equation:


Simplifying
-6x = 3x2 + 9

Reorder the terms:
-6x = 9 + 3x2

Solving
-6x = 9 + 3x2

Solving for variable 'x'.

Reorder the terms:
-9 + -6x + -3x2 = 9 + 3x2 + -9 + -3x2

Reorder the terms:
-9 + -6x + -3x2 = 9 + -9 + 3x2 + -3x2

Combine like terms: 9 + -9 = 0
-9 + -6x + -3x2 = 0 + 3x2 + -3x2
-9 + -6x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-9 + -6x + -3x2 = 0

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

Ignore the factor -3.

Subproblem 1

Set the factor '(3 + 2x + x2)' equal to zero and attempt to solve: Simplifying 3 + 2x + x2 = 0 Solving 3 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 2x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 2x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x + x2 = 0 + -3 2x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 2x + x2 = -3 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 = -3 + 1 Reorder the terms: 1 + 2x + x2 = -3 + 1 Combine like terms: -3 + 1 = -2 1 + 2x + x2 = -2 Factor a perfect square on the left side: (x + 1)(x + 1) = -2 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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