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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 = -1.133974596 x = -1.133974596 Simplifying x = -1.133974596Subproblem 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 = -2.866025404 x = -2.866025404 Simplifying x = -2.866025404Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.133974596, -2.866025404}Solution
x = {0, -1.133974596, -2.866025404}
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