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Simplifying 4x3 + -16x2 + 13x = 0 Reorder the terms: 13x + -16x2 + 4x3 = 0 Solving 13x + -16x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(13 + -16x + 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 '(13 + -16x + 4x2)' equal to zero and attempt to solve: Simplifying 13 + -16x + 4x2 = 0 Solving 13 + -16x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.25 + -4x + x2 = 0 Move the constant term to the right: Add '-3.25' to each side of the equation. 3.25 + -4x + -3.25 + x2 = 0 + -3.25 Reorder the terms: 3.25 + -3.25 + -4x + x2 = 0 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + -4x + x2 = 0 + -3.25 -4x + x2 = 0 + -3.25 Combine like terms: 0 + -3.25 = -3.25 -4x + x2 = -3.25 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 = -3.25 + 4 Reorder the terms: 4 + -4x + x2 = -3.25 + 4 Combine like terms: -3.25 + 4 = 0.75 4 + -4x + x2 = 0.75 Factor a perfect square on the left side: (x + -2)(x + -2) = 0.75 Calculate the square root of the right side: 0.866025404 Break this problem into two subproblems by setting (x + -2) equal to 0.866025404 and -0.866025404.Subproblem 1
x + -2 = 0.866025404 Simplifying x + -2 = 0.866025404 Reorder the terms: -2 + x = 0.866025404 Solving -2 + x = 0.866025404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0.866025404 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0.866025404 + 2 x = 0.866025404 + 2 Combine like terms: 0.866025404 + 2 = 2.866025404 x = 2.866025404 Simplifying x = 2.866025404Subproblem 2
x + -2 = -0.866025404 Simplifying x + -2 = -0.866025404 Reorder the terms: -2 + x = -0.866025404 Solving -2 + x = -0.866025404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -0.866025404 + 2 Combine like terms: -2 + 2 = 0 0 + x = -0.866025404 + 2 x = -0.866025404 + 2 Combine like terms: -0.866025404 + 2 = 1.133974596 x = 1.133974596 Simplifying x = 1.133974596Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.866025404, 1.133974596}Solution
x = {0, 2.866025404, 1.133974596}
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