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Simplifying 4x2 + 17x = 6x + -2x3 Reorder the terms: 17x + 4x2 = 6x + -2x3 Solving 17x + 4x2 = 6x + -2x3 Solving for variable 'x'. Reorder the terms: 17x + -6x + 4x2 + 2x3 = 6x + -2x3 + -6x + 2x3 Combine like terms: 17x + -6x = 11x 11x + 4x2 + 2x3 = 6x + -2x3 + -6x + 2x3 Reorder the terms: 11x + 4x2 + 2x3 = 6x + -6x + -2x3 + 2x3 Combine like terms: 6x + -6x = 0 11x + 4x2 + 2x3 = 0 + -2x3 + 2x3 11x + 4x2 + 2x3 = -2x3 + 2x3 Combine like terms: -2x3 + 2x3 = 0 11x + 4x2 + 2x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(11 + 4x + 2x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(11 + 4x + 2x2)' equal to zero and attempt to solve: Simplifying 11 + 4x + 2x2 = 0 Solving 11 + 4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5.5 + 2x + x2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + 2x + -5.5 + x2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + 2x + x2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + 2x + x2 = 0 + -5.5 2x + x2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 2x + x2 = -5.5 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 = -5.5 + 1 Reorder the terms: 1 + 2x + x2 = -5.5 + 1 Combine like terms: -5.5 + 1 = -4.5 1 + 2x + x2 = -4.5 Factor a perfect square on the left side: (x + 1)(x + 1) = -4.5 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.Solution
x = {0}
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