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Simplifying 28x3 + 56x2 + 13x = 0 Reorder the terms: 13x + 56x2 + 28x3 = 0 Solving 13x + 56x2 + 28x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(13 + 56x + 28x2) = 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 + 56x + 28x2)' equal to zero and attempt to solve: Simplifying 13 + 56x + 28x2 = 0 Solving 13 + 56x + 28x2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. 0.4642857143 + 2x + x2 = 0 Move the constant term to the right: Add '-0.4642857143' to each side of the equation. 0.4642857143 + 2x + -0.4642857143 + x2 = 0 + -0.4642857143 Reorder the terms: 0.4642857143 + -0.4642857143 + 2x + x2 = 0 + -0.4642857143 Combine like terms: 0.4642857143 + -0.4642857143 = 0.0000000000 0.0000000000 + 2x + x2 = 0 + -0.4642857143 2x + x2 = 0 + -0.4642857143 Combine like terms: 0 + -0.4642857143 = -0.4642857143 2x + x2 = -0.4642857143 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -0.4642857143 + 1 Reorder the terms: 1 + 2x + x2 = -0.4642857143 + 1 Combine like terms: -0.4642857143 + 1 = 0.5357142857 1 + 2x + x2 = 0.5357142857 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.5357142857 Calculate the square root of the right side: 0.731925055 Break this problem into two subproblems by setting (x + 1) equal to 0.731925055 and -0.731925055.Subproblem 1
x + 1 = 0.731925055 Simplifying x + 1 = 0.731925055 Reorder the terms: 1 + x = 0.731925055 Solving 1 + x = 0.731925055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.731925055 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.731925055 + -1 x = 0.731925055 + -1 Combine like terms: 0.731925055 + -1 = -0.268074945 x = -0.268074945 Simplifying x = -0.268074945Subproblem 2
x + 1 = -0.731925055 Simplifying x + 1 = -0.731925055 Reorder the terms: 1 + x = -0.731925055 Solving 1 + x = -0.731925055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.731925055 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.731925055 + -1 x = -0.731925055 + -1 Combine like terms: -0.731925055 + -1 = -1.731925055 x = -1.731925055 Simplifying x = -1.731925055Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.268074945, -1.731925055}Solution
x = {0, -0.268074945, -1.731925055}
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