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Simplifying (3x3 + -2x2 + 8x) + (7x3 + 6x2 + -13x) = 0 Reorder the terms: (8x + -2x2 + 3x3) + (7x3 + 6x2 + -13x) = 0 Remove parenthesis around (8x + -2x2 + 3x3) 8x + -2x2 + 3x3 + (7x3 + 6x2 + -13x) = 0 Reorder the terms: 8x + -2x2 + 3x3 + (-13x + 6x2 + 7x3) = 0 Remove parenthesis around (-13x + 6x2 + 7x3) 8x + -2x2 + 3x3 + -13x + 6x2 + 7x3 = 0 Reorder the terms: 8x + -13x + -2x2 + 6x2 + 3x3 + 7x3 = 0 Combine like terms: 8x + -13x = -5x -5x + -2x2 + 6x2 + 3x3 + 7x3 = 0 Combine like terms: -2x2 + 6x2 = 4x2 -5x + 4x2 + 3x3 + 7x3 = 0 Combine like terms: 3x3 + 7x3 = 10x3 -5x + 4x2 + 10x3 = 0 Solving -5x + 4x2 + 10x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-5 + 4x + 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 '(-5 + 4x + 10x2)' equal to zero and attempt to solve: Simplifying -5 + 4x + 10x2 = 0 Solving -5 + 4x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.5 + 0.4x + x2 = 0.0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.4x + 0.5 + x2 = 0.0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.4x + x2 = 0.0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.4x + x2 = 0.0 + 0.5 0.4x + x2 = 0.0 + 0.5 Combine like terms: 0.0 + 0.5 = 0.5 0.4x + x2 = 0.5 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 0.5 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 0.5 + 0.04 Combine like terms: 0.5 + 0.04 = 0.54 0.04 + 0.4x + x2 = 0.54 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 0.54 Calculate the square root of the right side: 0.734846923 Break this problem into two subproblems by setting (x + 0.2) equal to 0.734846923 and -0.734846923.Subproblem 1
x + 0.2 = 0.734846923 Simplifying x + 0.2 = 0.734846923 Reorder the terms: 0.2 + x = 0.734846923 Solving 0.2 + x = 0.734846923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 0.734846923 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.734846923 + -0.2 x = 0.734846923 + -0.2 Combine like terms: 0.734846923 + -0.2 = 0.534846923 x = 0.534846923 Simplifying x = 0.534846923Subproblem 2
x + 0.2 = -0.734846923 Simplifying x + 0.2 = -0.734846923 Reorder the terms: 0.2 + x = -0.734846923 Solving 0.2 + x = -0.734846923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -0.734846923 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.734846923 + -0.2 x = -0.734846923 + -0.2 Combine like terms: -0.734846923 + -0.2 = -0.934846923 x = -0.934846923 Simplifying x = -0.934846923Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.534846923, -0.934846923}Solution
x = {0, 0.534846923, -0.934846923}
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