3x^2-4x+6=-x^2+6x-2

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Solution for 3x^2-4x+6=-x^2+6x-2 equation:


Simplifying
3x2 + -4x + 6 = -1x2 + 6x + -2

Reorder the terms:
6 + -4x + 3x2 = -1x2 + 6x + -2

Reorder the terms:
6 + -4x + 3x2 = -2 + 6x + -1x2

Solving
6 + -4x + 3x2 = -2 + 6x + -1x2

Solving for variable 'x'.

Reorder the terms:
6 + 2 + -4x + -6x + 3x2 + x2 = -2 + 6x + -1x2 + 2 + -6x + x2

Combine like terms: 6 + 2 = 8
8 + -4x + -6x + 3x2 + x2 = -2 + 6x + -1x2 + 2 + -6x + x2

Combine like terms: -4x + -6x = -10x
8 + -10x + 3x2 + x2 = -2 + 6x + -1x2 + 2 + -6x + x2

Combine like terms: 3x2 + x2 = 4x2
8 + -10x + 4x2 = -2 + 6x + -1x2 + 2 + -6x + x2

Reorder the terms:
8 + -10x + 4x2 = -2 + 2 + 6x + -6x + -1x2 + x2

Combine like terms: -2 + 2 = 0
8 + -10x + 4x2 = 0 + 6x + -6x + -1x2 + x2
8 + -10x + 4x2 = 6x + -6x + -1x2 + x2

Combine like terms: 6x + -6x = 0
8 + -10x + 4x2 = 0 + -1x2 + x2
8 + -10x + 4x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
8 + -10x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -5x + 2x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(4 + -5x + 2x2)' equal to zero and attempt to solve: Simplifying 4 + -5x + 2x2 = 0 Solving 4 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + -2.5x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -2.5x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -2.5x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2.5x + x2 = 0 + -2 -2.5x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -2.5x + x2 = -2 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = -2 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -2 + 1.5625 Combine like terms: -2 + 1.5625 = -0.4375 1.5625 + -2.5x + x2 = -0.4375 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = -0.4375 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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