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Simplifying 6x3 + -6x2 + -56x = 0 Reorder the terms: -56x + -6x2 + 6x3 = 0 Solving -56x + -6x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-28 + -3x + 3x2) = 0 Ignore the factor 2.Subproblem 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 '(-28 + -3x + 3x2)' equal to zero and attempt to solve: Simplifying -28 + -3x + 3x2 = 0 Solving -28 + -3x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -9.333333333 + -1x + x2 = 0 Move the constant term to the right: Add '9.333333333' to each side of the equation. -9.333333333 + -1x + 9.333333333 + x2 = 0 + 9.333333333 Reorder the terms: -9.333333333 + 9.333333333 + -1x + x2 = 0 + 9.333333333 Combine like terms: -9.333333333 + 9.333333333 = 0.000000000 0.000000000 + -1x + x2 = 0 + 9.333333333 -1x + x2 = 0 + 9.333333333 Combine like terms: 0 + 9.333333333 = 9.333333333 -1x + x2 = 9.333333333 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 9.333333333 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 9.333333333 + 0.25 Combine like terms: 9.333333333 + 0.25 = 9.583333333 0.25 + -1x + x2 = 9.583333333 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 9.583333333 Calculate the square root of the right side: 3.095695937 Break this problem into two subproblems by setting (x + -0.5) equal to 3.095695937 and -3.095695937.Subproblem 1
x + -0.5 = 3.095695937 Simplifying x + -0.5 = 3.095695937 Reorder the terms: -0.5 + x = 3.095695937 Solving -0.5 + x = 3.095695937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 3.095695937 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.095695937 + 0.5 x = 3.095695937 + 0.5 Combine like terms: 3.095695937 + 0.5 = 3.595695937 x = 3.595695937 Simplifying x = 3.595695937Subproblem 2
x + -0.5 = -3.095695937 Simplifying x + -0.5 = -3.095695937 Reorder the terms: -0.5 + x = -3.095695937 Solving -0.5 + x = -3.095695937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -3.095695937 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.095695937 + 0.5 x = -3.095695937 + 0.5 Combine like terms: -3.095695937 + 0.5 = -2.595695937 x = -2.595695937 Simplifying x = -2.595695937Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.595695937, -2.595695937}Solution
x = {0, 3.595695937, -2.595695937}
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