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Simplifying (6x3 + -7x2 + 2x) + (8x3 + 9x2 + -11x) = 0 Reorder the terms: (2x + -7x2 + 6x3) + (8x3 + 9x2 + -11x) = 0 Remove parenthesis around (2x + -7x2 + 6x3) 2x + -7x2 + 6x3 + (8x3 + 9x2 + -11x) = 0 Reorder the terms: 2x + -7x2 + 6x3 + (-11x + 9x2 + 8x3) = 0 Remove parenthesis around (-11x + 9x2 + 8x3) 2x + -7x2 + 6x3 + -11x + 9x2 + 8x3 = 0 Reorder the terms: 2x + -11x + -7x2 + 9x2 + 6x3 + 8x3 = 0 Combine like terms: 2x + -11x = -9x -9x + -7x2 + 9x2 + 6x3 + 8x3 = 0 Combine like terms: -7x2 + 9x2 = 2x2 -9x + 2x2 + 6x3 + 8x3 = 0 Combine like terms: 6x3 + 8x3 = 14x3 -9x + 2x2 + 14x3 = 0 Solving -9x + 2x2 + 14x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-9 + 2x + 14x2) = 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 '(-9 + 2x + 14x2)' equal to zero and attempt to solve: Simplifying -9 + 2x + 14x2 = 0 Solving -9 + 2x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.6428571429 + 0.1428571429x + x2 = 0 Move the constant term to the right: Add '0.6428571429' to each side of the equation. -0.6428571429 + 0.1428571429x + 0.6428571429 + x2 = 0 + 0.6428571429 Reorder the terms: -0.6428571429 + 0.6428571429 + 0.1428571429x + x2 = 0 + 0.6428571429 Combine like terms: -0.6428571429 + 0.6428571429 = 0.0000000000 0.0000000000 + 0.1428571429x + x2 = 0 + 0.6428571429 0.1428571429x + x2 = 0 + 0.6428571429 Combine like terms: 0 + 0.6428571429 = 0.6428571429 0.1428571429x + x2 = 0.6428571429 The x term is 0.1428571429x. Take half its coefficient (0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. 0.1428571429x + 0.005102040819 + x2 = 0.6428571429 + 0.005102040819 Reorder the terms: 0.005102040819 + 0.1428571429x + x2 = 0.6428571429 + 0.005102040819 Combine like terms: 0.6428571429 + 0.005102040819 = 0.647959183719 0.005102040819 + 0.1428571429x + x2 = 0.647959183719 Factor a perfect square on the left side: (x + 0.07142857145)(x + 0.07142857145) = 0.647959183719 Calculate the square root of the right side: 0.804959119 Break this problem into two subproblems by setting (x + 0.07142857145) equal to 0.804959119 and -0.804959119.Subproblem 1
x + 0.07142857145 = 0.804959119 Simplifying x + 0.07142857145 = 0.804959119 Reorder the terms: 0.07142857145 + x = 0.804959119 Solving 0.07142857145 + x = 0.804959119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.07142857145' to each side of the equation. 0.07142857145 + -0.07142857145 + x = 0.804959119 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + x = 0.804959119 + -0.07142857145 x = 0.804959119 + -0.07142857145 Combine like terms: 0.804959119 + -0.07142857145 = 0.73353054755 x = 0.73353054755 Simplifying x = 0.73353054755Subproblem 2
x + 0.07142857145 = -0.804959119 Simplifying x + 0.07142857145 = -0.804959119 Reorder the terms: 0.07142857145 + x = -0.804959119 Solving 0.07142857145 + x = -0.804959119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.07142857145' to each side of the equation. 0.07142857145 + -0.07142857145 + x = -0.804959119 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + x = -0.804959119 + -0.07142857145 x = -0.804959119 + -0.07142857145 Combine like terms: -0.804959119 + -0.07142857145 = -0.87638769045 x = -0.87638769045 Simplifying x = -0.87638769045Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.73353054755, -0.87638769045}Solution
x = {0, 0.73353054755, -0.87638769045}
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