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Simplifying x3 + 4x2 + 7x = 0 Reorder the terms: 7x + 4x2 + x3 = 0 Solving 7x + 4x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(7 + 4x + x2) = 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 '(7 + 4x + x2)' equal to zero and attempt to solve: Simplifying 7 + 4x + x2 = 0 Solving 7 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 4x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 4x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4x + x2 = 0 + -7 4x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 4x + x2 = -7 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -7 + 4 Reorder the terms: 4 + 4x + x2 = -7 + 4 Combine like terms: -7 + 4 = -3 4 + 4x + x2 = -3 Factor a perfect square on the left side: (x + 2)(x + 2) = -3 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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