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Simplifying (5x3 + -6x2 + 2x) + (5x3 + 9x2 + -13x) = 0 Reorder the terms: (2x + -6x2 + 5x3) + (5x3 + 9x2 + -13x) = 0 Remove parenthesis around (2x + -6x2 + 5x3) 2x + -6x2 + 5x3 + (5x3 + 9x2 + -13x) = 0 Reorder the terms: 2x + -6x2 + 5x3 + (-13x + 9x2 + 5x3) = 0 Remove parenthesis around (-13x + 9x2 + 5x3) 2x + -6x2 + 5x3 + -13x + 9x2 + 5x3 = 0 Reorder the terms: 2x + -13x + -6x2 + 9x2 + 5x3 + 5x3 = 0 Combine like terms: 2x + -13x = -11x -11x + -6x2 + 9x2 + 5x3 + 5x3 = 0 Combine like terms: -6x2 + 9x2 = 3x2 -11x + 3x2 + 5x3 + 5x3 = 0 Combine like terms: 5x3 + 5x3 = 10x3 -11x + 3x2 + 10x3 = 0 Solving -11x + 3x2 + 10x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-11 + 3x + 10x2) = 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 '(-11 + 3x + 10x2)' equal to zero and attempt to solve: Simplifying -11 + 3x + 10x2 = 0 Solving -11 + 3x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.1 + 0.3x + x2 = 0.0 Move the constant term to the right: Add '1.1' to each side of the equation. -1.1 + 0.3x + 1.1 + x2 = 0.0 + 1.1 Reorder the terms: -1.1 + 1.1 + 0.3x + x2 = 0.0 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + 0.3x + x2 = 0.0 + 1.1 0.3x + x2 = 0.0 + 1.1 Combine like terms: 0.0 + 1.1 = 1.1 0.3x + x2 = 1.1 The x term is 0.3x. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3x + 0.0225 + x2 = 1.1 + 0.0225 Reorder the terms: 0.0225 + 0.3x + x2 = 1.1 + 0.0225 Combine like terms: 1.1 + 0.0225 = 1.1225 0.0225 + 0.3x + x2 = 1.1225 Factor a perfect square on the left side: (x + 0.15)(x + 0.15) = 1.1225 Calculate the square root of the right side: 1.059481005 Break this problem into two subproblems by setting (x + 0.15) equal to 1.059481005 and -1.059481005.Subproblem 1
x + 0.15 = 1.059481005 Simplifying x + 0.15 = 1.059481005 Reorder the terms: 0.15 + x = 1.059481005 Solving 0.15 + x = 1.059481005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = 1.059481005 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 1.059481005 + -0.15 x = 1.059481005 + -0.15 Combine like terms: 1.059481005 + -0.15 = 0.909481005 x = 0.909481005 Simplifying x = 0.909481005Subproblem 2
x + 0.15 = -1.059481005 Simplifying x + 0.15 = -1.059481005 Reorder the terms: 0.15 + x = -1.059481005 Solving 0.15 + x = -1.059481005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = -1.059481005 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -1.059481005 + -0.15 x = -1.059481005 + -0.15 Combine like terms: -1.059481005 + -0.15 = -1.209481005 x = -1.209481005 Simplifying x = -1.209481005Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.909481005, -1.209481005}Solution
x = {0, 0.909481005, -1.209481005}
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