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Simplifying x + 4 = kx2 + 2x + 5 Reorder the terms: 4 + x = kx2 + 2x + 5 Reorder the terms: 4 + x = 5 + kx2 + 2x Solving 4 + x = 5 + kx2 + 2x Solving for variable 'x'. Reorder the terms: 4 + -5 + -1kx2 + x + -2x = 5 + kx2 + 2x + -5 + -1kx2 + -2x Combine like terms: 4 + -5 = -1 -1 + -1kx2 + x + -2x = 5 + kx2 + 2x + -5 + -1kx2 + -2x Combine like terms: x + -2x = -1x -1 + -1kx2 + -1x = 5 + kx2 + 2x + -5 + -1kx2 + -2x Reorder the terms: -1 + -1kx2 + -1x = 5 + -5 + kx2 + -1kx2 + 2x + -2x Combine like terms: 5 + -5 = 0 -1 + -1kx2 + -1x = 0 + kx2 + -1kx2 + 2x + -2x -1 + -1kx2 + -1x = kx2 + -1kx2 + 2x + -2x Combine like terms: kx2 + -1kx2 = 0 -1 + -1kx2 + -1x = 0 + 2x + -2x -1 + -1kx2 + -1x = 2x + -2x Combine like terms: 2x + -2x = 0 -1 + -1kx2 + -1x = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + kx2 + x) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + kx2 + x)' equal to zero and attempt to solve: Simplifying 1 + kx2 + x = 0 Solving 1 + kx2 + x = 0 Begin completing the square. Divide all terms by k the coefficient of the squared term: Divide each side by 'k'. k-1 + x2 + k-1x = 0k-1 Move the constant term to the right: Add '-1' to each side of the equation. k-1 + x2 + -1 + k-1x = -1 + 0k-1 Reorder the terms: -1 + k-1 + k-1x + x2 = -1 + 0k-1 Combine like terms: -1 + 0 = -1 -1 + k-1 + k-1x + x2 = -1 The x term is k-1x. Take half its coefficient (0.5k-1). Square it (0.25k-2) and add it to both sides. Add '0.25k-2' to each side of the equation. -1 + k-1 + k-1x + 0.25k-2 + x2 = -1 + 0.25k-2 Reorder the terms: -1 + 0.25k-2 + k-1 + k-1x + x2 = -1 + 0.25k-2 Factor a perfect square on the left side: (x + 0.5k-1)(x + 0.5k-1) = -1 + 0.25k-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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