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Simplifying (8x3 + -3x2 + 2x) + (3x3 + 7x2 + -10x) = 0 Reorder the terms: (2x + -3x2 + 8x3) + (3x3 + 7x2 + -10x) = 0 Remove parenthesis around (2x + -3x2 + 8x3) 2x + -3x2 + 8x3 + (3x3 + 7x2 + -10x) = 0 Reorder the terms: 2x + -3x2 + 8x3 + (-10x + 7x2 + 3x3) = 0 Remove parenthesis around (-10x + 7x2 + 3x3) 2x + -3x2 + 8x3 + -10x + 7x2 + 3x3 = 0 Reorder the terms: 2x + -10x + -3x2 + 7x2 + 8x3 + 3x3 = 0 Combine like terms: 2x + -10x = -8x -8x + -3x2 + 7x2 + 8x3 + 3x3 = 0 Combine like terms: -3x2 + 7x2 = 4x2 -8x + 4x2 + 8x3 + 3x3 = 0 Combine like terms: 8x3 + 3x3 = 11x3 -8x + 4x2 + 11x3 = 0 Solving -8x + 4x2 + 11x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-8 + 4x + 11x2) = 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 '(-8 + 4x + 11x2)' equal to zero and attempt to solve: Simplifying -8 + 4x + 11x2 = 0 Solving -8 + 4x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.7272727273 + 0.3636363636x + x2 = 0 Move the constant term to the right: Add '0.7272727273' to each side of the equation. -0.7272727273 + 0.3636363636x + 0.7272727273 + x2 = 0 + 0.7272727273 Reorder the terms: -0.7272727273 + 0.7272727273 + 0.3636363636x + x2 = 0 + 0.7272727273 Combine like terms: -0.7272727273 + 0.7272727273 = 0.0000000000 0.0000000000 + 0.3636363636x + x2 = 0 + 0.7272727273 0.3636363636x + x2 = 0 + 0.7272727273 Combine like terms: 0 + 0.7272727273 = 0.7272727273 0.3636363636x + x2 = 0.7272727273 The x term is 0.3636363636x. Take half its coefficient (0.1818181818). Square it (0.03305785123) and add it to both sides. Add '0.03305785123' to each side of the equation. 0.3636363636x + 0.03305785123 + x2 = 0.7272727273 + 0.03305785123 Reorder the terms: 0.03305785123 + 0.3636363636x + x2 = 0.7272727273 + 0.03305785123 Combine like terms: 0.7272727273 + 0.03305785123 = 0.76033057853 0.03305785123 + 0.3636363636x + x2 = 0.76033057853 Factor a perfect square on the left side: (x + 0.1818181818)(x + 0.1818181818) = 0.76033057853 Calculate the square root of the right side: 0.871969368 Break this problem into two subproblems by setting (x + 0.1818181818) equal to 0.871969368 and -0.871969368.Subproblem 1
x + 0.1818181818 = 0.871969368 Simplifying x + 0.1818181818 = 0.871969368 Reorder the terms: 0.1818181818 + x = 0.871969368 Solving 0.1818181818 + x = 0.871969368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1818181818' to each side of the equation. 0.1818181818 + -0.1818181818 + x = 0.871969368 + -0.1818181818 Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000 0.0000000000 + x = 0.871969368 + -0.1818181818 x = 0.871969368 + -0.1818181818 Combine like terms: 0.871969368 + -0.1818181818 = 0.6901511862 x = 0.6901511862 Simplifying x = 0.6901511862Subproblem 2
x + 0.1818181818 = -0.871969368 Simplifying x + 0.1818181818 = -0.871969368 Reorder the terms: 0.1818181818 + x = -0.871969368 Solving 0.1818181818 + x = -0.871969368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1818181818' to each side of the equation. 0.1818181818 + -0.1818181818 + x = -0.871969368 + -0.1818181818 Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000 0.0000000000 + x = -0.871969368 + -0.1818181818 x = -0.871969368 + -0.1818181818 Combine like terms: -0.871969368 + -0.1818181818 = -1.0537875498 x = -1.0537875498 Simplifying x = -1.0537875498Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6901511862, -1.0537875498}Solution
x = {0, 0.6901511862, -1.0537875498}
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