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Simplifying (6x3 + 2x2 + 9x) + (-2x3 + 5x2 + 3x) = 0 Reorder the terms: (9x + 2x2 + 6x3) + (-2x3 + 5x2 + 3x) = 0 Remove parenthesis around (9x + 2x2 + 6x3) 9x + 2x2 + 6x3 + (-2x3 + 5x2 + 3x) = 0 Reorder the terms: 9x + 2x2 + 6x3 + (3x + 5x2 + -2x3) = 0 Remove parenthesis around (3x + 5x2 + -2x3) 9x + 2x2 + 6x3 + 3x + 5x2 + -2x3 = 0 Reorder the terms: 9x + 3x + 2x2 + 5x2 + 6x3 + -2x3 = 0 Combine like terms: 9x + 3x = 12x 12x + 2x2 + 5x2 + 6x3 + -2x3 = 0 Combine like terms: 2x2 + 5x2 = 7x2 12x + 7x2 + 6x3 + -2x3 = 0 Combine like terms: 6x3 + -2x3 = 4x3 12x + 7x2 + 4x3 = 0 Solving 12x + 7x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(12 + 7x + 4x2) = 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 '(12 + 7x + 4x2)' equal to zero and attempt to solve: Simplifying 12 + 7x + 4x2 = 0 Solving 12 + 7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3 + 1.75x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 1.75x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 1.75x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 1.75x + x2 = 0 + -3 1.75x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 1.75x + x2 = -3 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = -3 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = -3 + 0.765625 Combine like terms: -3 + 0.765625 = -2.234375 0.765625 + 1.75x + x2 = -2.234375 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = -2.234375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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