kx^2+2kx+x=0

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Solution for kx^2+2kx+x=0 equation:


Simplifying
kx2 + 2kx + x = 0

Reorder the terms:
2kx + kx2 + x = 0

Solving
2kx + kx2 + x = 0

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '-1x' to each side of the equation.
2kx + kx2 + x + -1x = 0 + -1x

Combine like terms: x + -1x = 0
2kx + kx2 + 0 = 0 + -1x
2kx + kx2 = 0 + -1x
Remove the zero:
2kx + kx2 = -1x

Combine like terms: -1x + x = 0
2kx + kx2 + x = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(2k + kx + 1) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing k to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(2k + kx + 1)' equal to zero and attempt to solve: Simplifying 2k + kx + 1 = 0 Reorder the terms: 1 + 2k + kx = 0 Solving 1 + 2k + kx = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 2k + -1 + kx = 0 + -1 Reorder the terms: 1 + -1 + 2k + kx = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2k + kx = 0 + -1 2k + kx = 0 + -1 Combine like terms: 0 + -1 = -1 2k + kx = -1 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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