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Simplifying x2 + 4x3 + 4x2 = -16x Reorder the terms: x2 + 4x2 + 4x3 = -16x Combine like terms: x2 + 4x2 = 5x2 5x2 + 4x3 = -16x Solving 5x2 + 4x3 = -16x Solving for variable 'x'. Reorder the terms: 16x + 5x2 + 4x3 = -16x + 16x Combine like terms: -16x + 16x = 0 16x + 5x2 + 4x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(16 + 5x + 4x2) = 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 '(16 + 5x + 4x2)' equal to zero and attempt to solve: Simplifying 16 + 5x + 4x2 = 0 Solving 16 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4 + 1.25x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 1.25x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 1.25x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 1.25x + x2 = 0 + -4 1.25x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 1.25x + x2 = -4 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = -4 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = -4 + 0.390625 Combine like terms: -4 + 0.390625 = -3.609375 0.390625 + 1.25x + x2 = -3.609375 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = -3.609375 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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