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Simplifying 13x3 + -36x = -12x2 Reorder the terms: -36x + 13x3 = -12x2 Solving -36x + 13x3 = -12x2 Solving for variable 'x'. Reorder the terms: -36x + 12x2 + 13x3 = -12x2 + 12x2 Combine like terms: -12x2 + 12x2 = 0 -36x + 12x2 + 13x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-36 + 12x + 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 '(-36 + 12x + 13x2)' equal to zero and attempt to solve: Simplifying -36 + 12x + 13x2 = 0 Solving -36 + 12x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -2.769230769 + 0.9230769231x + x2 = 0 Move the constant term to the right: Add '2.769230769' to each side of the equation. -2.769230769 + 0.9230769231x + 2.769230769 + x2 = 0 + 2.769230769 Reorder the terms: -2.769230769 + 2.769230769 + 0.9230769231x + x2 = 0 + 2.769230769 Combine like terms: -2.769230769 + 2.769230769 = 0.000000000 0.000000000 + 0.9230769231x + x2 = 0 + 2.769230769 0.9230769231x + x2 = 0 + 2.769230769 Combine like terms: 0 + 2.769230769 = 2.769230769 0.9230769231x + x2 = 2.769230769 The x term is 0.9230769231x. Take half its coefficient (0.4615384616). Square it (0.2130177515) and add it to both sides. Add '0.2130177515' to each side of the equation. 0.9230769231x + 0.2130177515 + x2 = 2.769230769 + 0.2130177515 Reorder the terms: 0.2130177515 + 0.9230769231x + x2 = 2.769230769 + 0.2130177515 Combine like terms: 2.769230769 + 0.2130177515 = 2.9822485205 0.2130177515 + 0.9230769231x + x2 = 2.9822485205 Factor a perfect square on the left side: (x + 0.4615384616)(x + 0.4615384616) = 2.9822485205 Calculate the square root of the right side: 1.726918794 Break this problem into two subproblems by setting (x + 0.4615384616) equal to 1.726918794 and -1.726918794.Subproblem 1
x + 0.4615384616 = 1.726918794 Simplifying x + 0.4615384616 = 1.726918794 Reorder the terms: 0.4615384616 + x = 1.726918794 Solving 0.4615384616 + x = 1.726918794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4615384616' to each side of the equation. 0.4615384616 + -0.4615384616 + x = 1.726918794 + -0.4615384616 Combine like terms: 0.4615384616 + -0.4615384616 = 0.0000000000 0.0000000000 + x = 1.726918794 + -0.4615384616 x = 1.726918794 + -0.4615384616 Combine like terms: 1.726918794 + -0.4615384616 = 1.2653803324 x = 1.2653803324 Simplifying x = 1.2653803324Subproblem 2
x + 0.4615384616 = -1.726918794 Simplifying x + 0.4615384616 = -1.726918794 Reorder the terms: 0.4615384616 + x = -1.726918794 Solving 0.4615384616 + x = -1.726918794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4615384616' to each side of the equation. 0.4615384616 + -0.4615384616 + x = -1.726918794 + -0.4615384616 Combine like terms: 0.4615384616 + -0.4615384616 = 0.0000000000 0.0000000000 + x = -1.726918794 + -0.4615384616 x = -1.726918794 + -0.4615384616 Combine like terms: -1.726918794 + -0.4615384616 = -2.1884572556 x = -2.1884572556 Simplifying x = -2.1884572556Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2653803324, -2.1884572556}Solution
x = {0, 1.2653803324, -2.1884572556}
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