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Simplifying 4x3 + 3x2 + -81x = 0 Reorder the terms: -81x + 3x2 + 4x3 = 0 Solving -81x + 3x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-81 + 3x + 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 '(-81 + 3x + 4x2)' equal to zero and attempt to solve: Simplifying -81 + 3x + 4x2 = 0 Solving -81 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -20.25 + 0.75x + x2 = 0 Move the constant term to the right: Add '20.25' to each side of the equation. -20.25 + 0.75x + 20.25 + x2 = 0 + 20.25 Reorder the terms: -20.25 + 20.25 + 0.75x + x2 = 0 + 20.25 Combine like terms: -20.25 + 20.25 = 0.00 0.00 + 0.75x + x2 = 0 + 20.25 0.75x + x2 = 0 + 20.25 Combine like terms: 0 + 20.25 = 20.25 0.75x + x2 = 20.25 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 20.25 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 20.25 + 0.140625 Combine like terms: 20.25 + 0.140625 = 20.390625 0.140625 + 0.75x + x2 = 20.390625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 20.390625 Calculate the square root of the right side: 4.515597967 Break this problem into two subproblems by setting (x + 0.375) equal to 4.515597967 and -4.515597967.Subproblem 1
x + 0.375 = 4.515597967 Simplifying x + 0.375 = 4.515597967 Reorder the terms: 0.375 + x = 4.515597967 Solving 0.375 + x = 4.515597967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 4.515597967 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 4.515597967 + -0.375 x = 4.515597967 + -0.375 Combine like terms: 4.515597967 + -0.375 = 4.140597967 x = 4.140597967 Simplifying x = 4.140597967Subproblem 2
x + 0.375 = -4.515597967 Simplifying x + 0.375 = -4.515597967 Reorder the terms: 0.375 + x = -4.515597967 Solving 0.375 + x = -4.515597967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -4.515597967 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -4.515597967 + -0.375 x = -4.515597967 + -0.375 Combine like terms: -4.515597967 + -0.375 = -4.890597967 x = -4.890597967 Simplifying x = -4.890597967Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.140597967, -4.890597967}Solution
x = {0, 4.140597967, -4.890597967}
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