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Simplifying (5x3 + -4x2 + 6x) + (5x3 + 7x2 + -11x) = 0 Reorder the terms: (6x + -4x2 + 5x3) + (5x3 + 7x2 + -11x) = 0 Remove parenthesis around (6x + -4x2 + 5x3) 6x + -4x2 + 5x3 + (5x3 + 7x2 + -11x) = 0 Reorder the terms: 6x + -4x2 + 5x3 + (-11x + 7x2 + 5x3) = 0 Remove parenthesis around (-11x + 7x2 + 5x3) 6x + -4x2 + 5x3 + -11x + 7x2 + 5x3 = 0 Reorder the terms: 6x + -11x + -4x2 + 7x2 + 5x3 + 5x3 = 0 Combine like terms: 6x + -11x = -5x -5x + -4x2 + 7x2 + 5x3 + 5x3 = 0 Combine like terms: -4x2 + 7x2 = 3x2 -5x + 3x2 + 5x3 + 5x3 = 0 Combine like terms: 5x3 + 5x3 = 10x3 -5x + 3x2 + 10x3 = 0 Solving -5x + 3x2 + 10x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-5 + 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 '(-5 + 3x + 10x2)' equal to zero and attempt to solve: Simplifying -5 + 3x + 10x2 = 0 Solving -5 + 3x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.5 + 0.3x + x2 = 0.0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.3x + 0.5 + x2 = 0.0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.3x + x2 = 0.0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.3x + x2 = 0.0 + 0.5 0.3x + x2 = 0.0 + 0.5 Combine like terms: 0.0 + 0.5 = 0.5 0.3x + x2 = 0.5 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 = 0.5 + 0.0225 Reorder the terms: 0.0225 + 0.3x + x2 = 0.5 + 0.0225 Combine like terms: 0.5 + 0.0225 = 0.5225 0.0225 + 0.3x + x2 = 0.5225 Factor a perfect square on the left side: (x + 0.15)(x + 0.15) = 0.5225 Calculate the square root of the right side: 0.722841615 Break this problem into two subproblems by setting (x + 0.15) equal to 0.722841615 and -0.722841615.Subproblem 1
x + 0.15 = 0.722841615 Simplifying x + 0.15 = 0.722841615 Reorder the terms: 0.15 + x = 0.722841615 Solving 0.15 + x = 0.722841615 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 = 0.722841615 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 0.722841615 + -0.15 x = 0.722841615 + -0.15 Combine like terms: 0.722841615 + -0.15 = 0.572841615 x = 0.572841615 Simplifying x = 0.572841615Subproblem 2
x + 0.15 = -0.722841615 Simplifying x + 0.15 = -0.722841615 Reorder the terms: 0.15 + x = -0.722841615 Solving 0.15 + x = -0.722841615 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 = -0.722841615 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -0.722841615 + -0.15 x = -0.722841615 + -0.15 Combine like terms: -0.722841615 + -0.15 = -0.872841615 x = -0.872841615 Simplifying x = -0.872841615Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.572841615, -0.872841615}Solution
x = {0, 0.572841615, -0.872841615}
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