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Simplifying 3x3 + -13x2 + 13x = 0 Reorder the terms: 13x + -13x2 + 3x3 = 0 Solving 13x + -13x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(13 + -13x + 3x2) = 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 + -13x + 3x2)' equal to zero and attempt to solve: Simplifying 13 + -13x + 3x2 = 0 Solving 13 + -13x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4.333333333 + -4.333333333x + x2 = 0 Move the constant term to the right: Add '-4.333333333' to each side of the equation. 4.333333333 + -4.333333333x + -4.333333333 + x2 = 0 + -4.333333333 Reorder the terms: 4.333333333 + -4.333333333 + -4.333333333x + x2 = 0 + -4.333333333 Combine like terms: 4.333333333 + -4.333333333 = 0.000000000 0.000000000 + -4.333333333x + x2 = 0 + -4.333333333 -4.333333333x + x2 = 0 + -4.333333333 Combine like terms: 0 + -4.333333333 = -4.333333333 -4.333333333x + x2 = -4.333333333 The x term is -4.333333333x. Take half its coefficient (-2.166666667). Square it (4.694444446) and add it to both sides. Add '4.694444446' to each side of the equation. -4.333333333x + 4.694444446 + x2 = -4.333333333 + 4.694444446 Reorder the terms: 4.694444446 + -4.333333333x + x2 = -4.333333333 + 4.694444446 Combine like terms: -4.333333333 + 4.694444446 = 0.361111113 4.694444446 + -4.333333333x + x2 = 0.361111113 Factor a perfect square on the left side: (x + -2.166666667)(x + -2.166666667) = 0.361111113 Calculate the square root of the right side: 0.600925214 Break this problem into two subproblems by setting (x + -2.166666667) equal to 0.600925214 and -0.600925214.Subproblem 1
x + -2.166666667 = 0.600925214 Simplifying x + -2.166666667 = 0.600925214 Reorder the terms: -2.166666667 + x = 0.600925214 Solving -2.166666667 + x = 0.600925214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + x = 0.600925214 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = 0.600925214 + 2.166666667 x = 0.600925214 + 2.166666667 Combine like terms: 0.600925214 + 2.166666667 = 2.767591881 x = 2.767591881 Simplifying x = 2.767591881Subproblem 2
x + -2.166666667 = -0.600925214 Simplifying x + -2.166666667 = -0.600925214 Reorder the terms: -2.166666667 + x = -0.600925214 Solving -2.166666667 + x = -0.600925214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + x = -0.600925214 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = -0.600925214 + 2.166666667 x = -0.600925214 + 2.166666667 Combine like terms: -0.600925214 + 2.166666667 = 1.565741453 x = 1.565741453 Simplifying x = 1.565741453Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.767591881, 1.565741453}Solution
x = {0, 2.767591881, 1.565741453}
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