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Simplifying (6x3 + -5x2 + 7x) + (2x3 + 7x2 + -14x) = 0 Reorder the terms: (7x + -5x2 + 6x3) + (2x3 + 7x2 + -14x) = 0 Remove parenthesis around (7x + -5x2 + 6x3) 7x + -5x2 + 6x3 + (2x3 + 7x2 + -14x) = 0 Reorder the terms: 7x + -5x2 + 6x3 + (-14x + 7x2 + 2x3) = 0 Remove parenthesis around (-14x + 7x2 + 2x3) 7x + -5x2 + 6x3 + -14x + 7x2 + 2x3 = 0 Reorder the terms: 7x + -14x + -5x2 + 7x2 + 6x3 + 2x3 = 0 Combine like terms: 7x + -14x = -7x -7x + -5x2 + 7x2 + 6x3 + 2x3 = 0 Combine like terms: -5x2 + 7x2 = 2x2 -7x + 2x2 + 6x3 + 2x3 = 0 Combine like terms: 6x3 + 2x3 = 8x3 -7x + 2x2 + 8x3 = 0 Solving -7x + 2x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-7 + 2x + 8x2) = 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 '(-7 + 2x + 8x2)' equal to zero and attempt to solve: Simplifying -7 + 2x + 8x2 = 0 Solving -7 + 2x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.875 + 0.25x + x2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + 0.25x + 0.875 + x2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + 0.25x + x2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + 0.25x + x2 = 0 + 0.875 0.25x + x2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 0.25x + x2 = 0.875 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 0.875 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 0.875 + 0.015625 Combine like terms: 0.875 + 0.015625 = 0.890625 0.015625 + 0.25x + x2 = 0.890625 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 0.890625 Calculate the square root of the right side: 0.943729304 Break this problem into two subproblems by setting (x + 0.125) equal to 0.943729304 and -0.943729304.Subproblem 1
x + 0.125 = 0.943729304 Simplifying x + 0.125 = 0.943729304 Reorder the terms: 0.125 + x = 0.943729304 Solving 0.125 + x = 0.943729304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 0.943729304 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 0.943729304 + -0.125 x = 0.943729304 + -0.125 Combine like terms: 0.943729304 + -0.125 = 0.818729304 x = 0.818729304 Simplifying x = 0.818729304Subproblem 2
x + 0.125 = -0.943729304 Simplifying x + 0.125 = -0.943729304 Reorder the terms: 0.125 + x = -0.943729304 Solving 0.125 + x = -0.943729304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -0.943729304 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -0.943729304 + -0.125 x = -0.943729304 + -0.125 Combine like terms: -0.943729304 + -0.125 = -1.068729304 x = -1.068729304 Simplifying x = -1.068729304Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.818729304, -1.068729304}Solution
x = {0, 0.818729304, -1.068729304}
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