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Simplifying (6x3 + -5x2 + 3x) + (5x3 + 7x2 + -11x) = 0 Reorder the terms: (3x + -5x2 + 6x3) + (5x3 + 7x2 + -11x) = 0 Remove parenthesis around (3x + -5x2 + 6x3) 3x + -5x2 + 6x3 + (5x3 + 7x2 + -11x) = 0 Reorder the terms: 3x + -5x2 + 6x3 + (-11x + 7x2 + 5x3) = 0 Remove parenthesis around (-11x + 7x2 + 5x3) 3x + -5x2 + 6x3 + -11x + 7x2 + 5x3 = 0 Reorder the terms: 3x + -11x + -5x2 + 7x2 + 6x3 + 5x3 = 0 Combine like terms: 3x + -11x = -8x -8x + -5x2 + 7x2 + 6x3 + 5x3 = 0 Combine like terms: -5x2 + 7x2 = 2x2 -8x + 2x2 + 6x3 + 5x3 = 0 Combine like terms: 6x3 + 5x3 = 11x3 -8x + 2x2 + 11x3 = 0 Solving -8x + 2x2 + 11x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-8 + 2x + 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 + 2x + 11x2)' equal to zero and attempt to solve: Simplifying -8 + 2x + 11x2 = 0 Solving -8 + 2x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.7272727273 + 0.1818181818x + x2 = 0 Move the constant term to the right: Add '0.7272727273' to each side of the equation. -0.7272727273 + 0.1818181818x + 0.7272727273 + x2 = 0 + 0.7272727273 Reorder the terms: -0.7272727273 + 0.7272727273 + 0.1818181818x + x2 = 0 + 0.7272727273 Combine like terms: -0.7272727273 + 0.7272727273 = 0.0000000000 0.0000000000 + 0.1818181818x + x2 = 0 + 0.7272727273 0.1818181818x + x2 = 0 + 0.7272727273 Combine like terms: 0 + 0.7272727273 = 0.7272727273 0.1818181818x + x2 = 0.7272727273 The x term is 0.1818181818x. Take half its coefficient (0.0909090909). Square it (0.008264462808) and add it to both sides. Add '0.008264462808' to each side of the equation. 0.1818181818x + 0.008264462808 + x2 = 0.7272727273 + 0.008264462808 Reorder the terms: 0.008264462808 + 0.1818181818x + x2 = 0.7272727273 + 0.008264462808 Combine like terms: 0.7272727273 + 0.008264462808 = 0.735537190108 0.008264462808 + 0.1818181818x + x2 = 0.735537190108 Factor a perfect square on the left side: (x + 0.0909090909)(x + 0.0909090909) = 0.735537190108 Calculate the square root of the right side: 0.857634648 Break this problem into two subproblems by setting (x + 0.0909090909) equal to 0.857634648 and -0.857634648.Subproblem 1
x + 0.0909090909 = 0.857634648 Simplifying x + 0.0909090909 = 0.857634648 Reorder the terms: 0.0909090909 + x = 0.857634648 Solving 0.0909090909 + x = 0.857634648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0909090909' to each side of the equation. 0.0909090909 + -0.0909090909 + x = 0.857634648 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = 0.857634648 + -0.0909090909 x = 0.857634648 + -0.0909090909 Combine like terms: 0.857634648 + -0.0909090909 = 0.7667255571 x = 0.7667255571 Simplifying x = 0.7667255571Subproblem 2
x + 0.0909090909 = -0.857634648 Simplifying x + 0.0909090909 = -0.857634648 Reorder the terms: 0.0909090909 + x = -0.857634648 Solving 0.0909090909 + x = -0.857634648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0909090909' to each side of the equation. 0.0909090909 + -0.0909090909 + x = -0.857634648 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = -0.857634648 + -0.0909090909 x = -0.857634648 + -0.0909090909 Combine like terms: -0.857634648 + -0.0909090909 = -0.9485437389 x = -0.9485437389 Simplifying x = -0.9485437389Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7667255571, -0.9485437389}Solution
x = {0, 0.7667255571, -0.9485437389}
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