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Simplifying 4x3 + 22x2 + 52x = 0 Reorder the terms: 52x + 22x2 + 4x3 = 0 Solving 52x + 22x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(26 + 11x + 2x2) = 0 Ignore the factor 2.Subproblem 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 '(26 + 11x + 2x2)' equal to zero and attempt to solve: Simplifying 26 + 11x + 2x2 = 0 Solving 26 + 11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 13 + 5.5x + x2 = 0 Move the constant term to the right: Add '-13' to each side of the equation. 13 + 5.5x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + 5.5x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 5.5x + x2 = 0 + -13 5.5x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 5.5x + x2 = -13 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = -13 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = -13 + 7.5625 Combine like terms: -13 + 7.5625 = -5.4375 7.5625 + 5.5x + x2 = -5.4375 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = -5.4375 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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