6=-2x^2+4x

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


Simplifying
6 = -2x2 + 4x

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

Solving
6 = 4x + -2x2

Solving for variable 'x'.

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

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

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

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

Ignore the factor 2.

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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