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Simplifying (2k + 2) * x2 + -4kx + 4 = 0 Reorder the terms: (2 + 2k) * x2 + -4kx + 4 = 0 Reorder the terms for easier multiplication: x2(2 + 2k) + -4kx + 4 = 0 (2 * x2 + 2k * x2) + -4kx + 4 = 0 Reorder the terms: (2kx2 + 2x2) + -4kx + 4 = 0 (2kx2 + 2x2) + -4kx + 4 = 0 Reorder the terms: 4 + -4kx + 2kx2 + 2x2 = 0 Solving 4 + -4kx + 2kx2 + 2x2 = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4kx + 2kx2 + -4 + 2x2 = 0 + -4 Reorder the terms: 4 + -4 + -4kx + 2kx2 + 2x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -4kx + 2kx2 + 2x2 = 0 + -4 -4kx + 2kx2 + 2x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -4kx + 2kx2 + 2x2 = -4 Add '-2x2' to each side of the equation. -4kx + 2kx2 + 2x2 + -2x2 = -4 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -4kx + 2kx2 + 0 = -4 + -2x2 -4kx + 2kx2 = -4 + -2x2 Reorder the terms: 4 + -4kx + 2kx2 + 2x2 = -4 + -2x2 + 4 + 2x2 Reorder the terms: 4 + -4kx + 2kx2 + 2x2 = -4 + 4 + -2x2 + 2x2 Combine like terms: -4 + 4 = 0 4 + -4kx + 2kx2 + 2x2 = 0 + -2x2 + 2x2 4 + -4kx + 2kx2 + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 4 + -4kx + 2kx2 + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -2kx + kx2 + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -2kx + kx2 + x2)' equal to zero and attempt to solve: Simplifying 2 + -2kx + kx2 + x2 = 0 Solving 2 + -2kx + kx2 + x2 = 0 Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2kx + kx2 + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -2kx + kx2 + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2kx + kx2 + x2 = 0 + -2 -2kx + kx2 + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -2kx + kx2 + x2 = -2 Add '-1x2' to each side of the equation. -2kx + kx2 + x2 + -1x2 = -2 + -1x2 Combine like terms: x2 + -1x2 = 0 -2kx + kx2 + 0 = -2 + -1x2 -2kx + kx2 = -2 + -1x2 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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