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Simplifying 4x3 + -13x2 + -16x = 0 Reorder the terms: -16x + -13x2 + 4x3 = 0 Solving -16x + -13x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-16 + -13x + 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 + -13x + 4x2)' equal to zero and attempt to solve: Simplifying -16 + -13x + 4x2 = 0 Solving -16 + -13x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4 + -3.25x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -3.25x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -3.25x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3.25x + x2 = 0 + 4 -3.25x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -3.25x + x2 = 4 The x term is -3.25x. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25x + 2.640625 + x2 = 4 + 2.640625 Reorder the terms: 2.640625 + -3.25x + x2 = 4 + 2.640625 Combine like terms: 4 + 2.640625 = 6.640625 2.640625 + -3.25x + x2 = 6.640625 Factor a perfect square on the left side: (x + -1.625)(x + -1.625) = 6.640625 Calculate the square root of the right side: 2.576941016 Break this problem into two subproblems by setting (x + -1.625) equal to 2.576941016 and -2.576941016.Subproblem 1
x + -1.625 = 2.576941016 Simplifying x + -1.625 = 2.576941016 Reorder the terms: -1.625 + x = 2.576941016 Solving -1.625 + x = 2.576941016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = 2.576941016 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = 2.576941016 + 1.625 x = 2.576941016 + 1.625 Combine like terms: 2.576941016 + 1.625 = 4.201941016 x = 4.201941016 Simplifying x = 4.201941016Subproblem 2
x + -1.625 = -2.576941016 Simplifying x + -1.625 = -2.576941016 Reorder the terms: -1.625 + x = -2.576941016 Solving -1.625 + x = -2.576941016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = -2.576941016 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = -2.576941016 + 1.625 x = -2.576941016 + 1.625 Combine like terms: -2.576941016 + 1.625 = -0.951941016 x = -0.951941016 Simplifying x = -0.951941016Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.201941016, -0.951941016}Solution
x = {0, 4.201941016, -0.951941016}
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