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Simplifying (6x3 + -6x2 + 5x) + (7x3 + 9x2 + -11x) = 0 Reorder the terms: (5x + -6x2 + 6x3) + (7x3 + 9x2 + -11x) = 0 Remove parenthesis around (5x + -6x2 + 6x3) 5x + -6x2 + 6x3 + (7x3 + 9x2 + -11x) = 0 Reorder the terms: 5x + -6x2 + 6x3 + (-11x + 9x2 + 7x3) = 0 Remove parenthesis around (-11x + 9x2 + 7x3) 5x + -6x2 + 6x3 + -11x + 9x2 + 7x3 = 0 Reorder the terms: 5x + -11x + -6x2 + 9x2 + 6x3 + 7x3 = 0 Combine like terms: 5x + -11x = -6x -6x + -6x2 + 9x2 + 6x3 + 7x3 = 0 Combine like terms: -6x2 + 9x2 = 3x2 -6x + 3x2 + 6x3 + 7x3 = 0 Combine like terms: 6x3 + 7x3 = 13x3 -6x + 3x2 + 13x3 = 0 Solving -6x + 3x2 + 13x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-6 + 3x + 13x2) = 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 '(-6 + 3x + 13x2)' equal to zero and attempt to solve: Simplifying -6 + 3x + 13x2 = 0 Solving -6 + 3x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -0.4615384615 + 0.2307692308x + x2 = 0 Move the constant term to the right: Add '0.4615384615' to each side of the equation. -0.4615384615 + 0.2307692308x + 0.4615384615 + x2 = 0 + 0.4615384615 Reorder the terms: -0.4615384615 + 0.4615384615 + 0.2307692308x + x2 = 0 + 0.4615384615 Combine like terms: -0.4615384615 + 0.4615384615 = 0.0000000000 0.0000000000 + 0.2307692308x + x2 = 0 + 0.4615384615 0.2307692308x + x2 = 0 + 0.4615384615 Combine like terms: 0 + 0.4615384615 = 0.4615384615 0.2307692308x + x2 = 0.4615384615 The x term is 0.2307692308x. Take half its coefficient (0.1153846154). Square it (0.01331360947) and add it to both sides. Add '0.01331360947' to each side of the equation. 0.2307692308x + 0.01331360947 + x2 = 0.4615384615 + 0.01331360947 Reorder the terms: 0.01331360947 + 0.2307692308x + x2 = 0.4615384615 + 0.01331360947 Combine like terms: 0.4615384615 + 0.01331360947 = 0.47485207097 0.01331360947 + 0.2307692308x + x2 = 0.47485207097 Factor a perfect square on the left side: (x + 0.1153846154)(x + 0.1153846154) = 0.47485207097 Calculate the square root of the right side: 0.68909511 Break this problem into two subproblems by setting (x + 0.1153846154) equal to 0.68909511 and -0.68909511.Subproblem 1
x + 0.1153846154 = 0.68909511 Simplifying x + 0.1153846154 = 0.68909511 Reorder the terms: 0.1153846154 + x = 0.68909511 Solving 0.1153846154 + x = 0.68909511 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1153846154' to each side of the equation. 0.1153846154 + -0.1153846154 + x = 0.68909511 + -0.1153846154 Combine like terms: 0.1153846154 + -0.1153846154 = 0.0000000000 0.0000000000 + x = 0.68909511 + -0.1153846154 x = 0.68909511 + -0.1153846154 Combine like terms: 0.68909511 + -0.1153846154 = 0.5737104946 x = 0.5737104946 Simplifying x = 0.5737104946Subproblem 2
x + 0.1153846154 = -0.68909511 Simplifying x + 0.1153846154 = -0.68909511 Reorder the terms: 0.1153846154 + x = -0.68909511 Solving 0.1153846154 + x = -0.68909511 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1153846154' to each side of the equation. 0.1153846154 + -0.1153846154 + x = -0.68909511 + -0.1153846154 Combine like terms: 0.1153846154 + -0.1153846154 = 0.0000000000 0.0000000000 + x = -0.68909511 + -0.1153846154 x = -0.68909511 + -0.1153846154 Combine like terms: -0.68909511 + -0.1153846154 = -0.8044797254 x = -0.8044797254 Simplifying x = -0.8044797254Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5737104946, -0.8044797254}Solution
x = {0, 0.5737104946, -0.8044797254}
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