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Simplifying (9x3 + -6x2 + 6x) + (3x3 + 9x2 + -14x) = 0 Reorder the terms: (6x + -6x2 + 9x3) + (3x3 + 9x2 + -14x) = 0 Remove parenthesis around (6x + -6x2 + 9x3) 6x + -6x2 + 9x3 + (3x3 + 9x2 + -14x) = 0 Reorder the terms: 6x + -6x2 + 9x3 + (-14x + 9x2 + 3x3) = 0 Remove parenthesis around (-14x + 9x2 + 3x3) 6x + -6x2 + 9x3 + -14x + 9x2 + 3x3 = 0 Reorder the terms: 6x + -14x + -6x2 + 9x2 + 9x3 + 3x3 = 0 Combine like terms: 6x + -14x = -8x -8x + -6x2 + 9x2 + 9x3 + 3x3 = 0 Combine like terms: -6x2 + 9x2 = 3x2 -8x + 3x2 + 9x3 + 3x3 = 0 Combine like terms: 9x3 + 3x3 = 12x3 -8x + 3x2 + 12x3 = 0 Solving -8x + 3x2 + 12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-8 + 3x + 12x2) = 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 + 3x + 12x2)' equal to zero and attempt to solve: Simplifying -8 + 3x + 12x2 = 0 Solving -8 + 3x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.6666666667 + 0.25x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 0.25x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 0.25x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 0.25x + x2 = 0 + 0.6666666667 0.25x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 0.25x + x2 = 0.6666666667 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 = 0.6666666667 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 0.6666666667 + 0.015625 Combine like terms: 0.6666666667 + 0.015625 = 0.6822916667 0.015625 + 0.25x + x2 = 0.6822916667 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 0.6822916667 Calculate the square root of the right side: 0.826009483 Break this problem into two subproblems by setting (x + 0.125) equal to 0.826009483 and -0.826009483.Subproblem 1
x + 0.125 = 0.826009483 Simplifying x + 0.125 = 0.826009483 Reorder the terms: 0.125 + x = 0.826009483 Solving 0.125 + x = 0.826009483 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 = 0.826009483 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 0.826009483 + -0.125 x = 0.826009483 + -0.125 Combine like terms: 0.826009483 + -0.125 = 0.701009483 x = 0.701009483 Simplifying x = 0.701009483Subproblem 2
x + 0.125 = -0.826009483 Simplifying x + 0.125 = -0.826009483 Reorder the terms: 0.125 + x = -0.826009483 Solving 0.125 + x = -0.826009483 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 = -0.826009483 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -0.826009483 + -0.125 x = -0.826009483 + -0.125 Combine like terms: -0.826009483 + -0.125 = -0.951009483 x = -0.951009483 Simplifying x = -0.951009483Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.701009483, -0.951009483}Solution
x = {0, 0.701009483, -0.951009483}
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