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Simplifying 4x3 + -11x2 + -6x = 0 Reorder the terms: -6x + -11x2 + 4x3 = 0 Solving -6x + -11x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-6 + -11x + 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 '(-6 + -11x + 4x2)' equal to zero and attempt to solve: Simplifying -6 + -11x + 4x2 = 0 Solving -6 + -11x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.5 + -2.75x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -2.75x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -2.75x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -2.75x + x2 = 0 + 1.5 -2.75x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -2.75x + x2 = 1.5 The x term is -2.75x. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75x + 1.890625 + x2 = 1.5 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 1.5 + 1.890625 Combine like terms: 1.5 + 1.890625 = 3.390625 1.890625 + -2.75x + x2 = 3.390625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 3.390625 Calculate the square root of the right side: 1.841364983 Break this problem into two subproblems by setting (x + -1.375) equal to 1.841364983 and -1.841364983.Subproblem 1
x + -1.375 = 1.841364983 Simplifying x + -1.375 = 1.841364983 Reorder the terms: -1.375 + x = 1.841364983 Solving -1.375 + x = 1.841364983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 1.841364983 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 1.841364983 + 1.375 x = 1.841364983 + 1.375 Combine like terms: 1.841364983 + 1.375 = 3.216364983 x = 3.216364983 Simplifying x = 3.216364983Subproblem 2
x + -1.375 = -1.841364983 Simplifying x + -1.375 = -1.841364983 Reorder the terms: -1.375 + x = -1.841364983 Solving -1.375 + x = -1.841364983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -1.841364983 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -1.841364983 + 1.375 x = -1.841364983 + 1.375 Combine like terms: -1.841364983 + 1.375 = -0.466364983 x = -0.466364983 Simplifying x = -0.466364983Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.216364983, -0.466364983}Solution
x = {0, 3.216364983, -0.466364983}
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