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Simplifying 3x(x2 + 2x + -2) + 2x(3x2 + -1x + -4) = 0 Reorder the terms: 3x(-2 + 2x + x2) + 2x(3x2 + -1x + -4) = 0 (-2 * 3x + 2x * 3x + x2 * 3x) + 2x(3x2 + -1x + -4) = 0 (-6x + 6x2 + 3x3) + 2x(3x2 + -1x + -4) = 0 Reorder the terms: -6x + 6x2 + 3x3 + 2x(-4 + -1x + 3x2) = 0 -6x + 6x2 + 3x3 + (-4 * 2x + -1x * 2x + 3x2 * 2x) = 0 -6x + 6x2 + 3x3 + (-8x + -2x2 + 6x3) = 0 Reorder the terms: -6x + -8x + 6x2 + -2x2 + 3x3 + 6x3 = 0 Combine like terms: -6x + -8x = -14x -14x + 6x2 + -2x2 + 3x3 + 6x3 = 0 Combine like terms: 6x2 + -2x2 = 4x2 -14x + 4x2 + 3x3 + 6x3 = 0 Combine like terms: 3x3 + 6x3 = 9x3 -14x + 4x2 + 9x3 = 0 Solving -14x + 4x2 + 9x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-14 + 4x + 9x2) = 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 '(-14 + 4x + 9x2)' equal to zero and attempt to solve: Simplifying -14 + 4x + 9x2 = 0 Solving -14 + 4x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.555555556 + 0.4444444444x + x2 = 0 Move the constant term to the right: Add '1.555555556' to each side of the equation. -1.555555556 + 0.4444444444x + 1.555555556 + x2 = 0 + 1.555555556 Reorder the terms: -1.555555556 + 1.555555556 + 0.4444444444x + x2 = 0 + 1.555555556 Combine like terms: -1.555555556 + 1.555555556 = 0.000000000 0.000000000 + 0.4444444444x + x2 = 0 + 1.555555556 0.4444444444x + x2 = 0 + 1.555555556 Combine like terms: 0 + 1.555555556 = 1.555555556 0.4444444444x + x2 = 1.555555556 The x term is 0.4444444444x. Take half its coefficient (0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. 0.4444444444x + 0.04938271604 + x2 = 1.555555556 + 0.04938271604 Reorder the terms: 0.04938271604 + 0.4444444444x + x2 = 1.555555556 + 0.04938271604 Combine like terms: 1.555555556 + 0.04938271604 = 1.60493827204 0.04938271604 + 0.4444444444x + x2 = 1.60493827204 Factor a perfect square on the left side: (x + 0.2222222222)(x + 0.2222222222) = 1.60493827204 Calculate the square root of the right side: 1.266861584 Break this problem into two subproblems by setting (x + 0.2222222222) equal to 1.266861584 and -1.266861584.Subproblem 1
x + 0.2222222222 = 1.266861584 Simplifying x + 0.2222222222 = 1.266861584 Reorder the terms: 0.2222222222 + x = 1.266861584 Solving 0.2222222222 + x = 1.266861584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = 1.266861584 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = 1.266861584 + -0.2222222222 x = 1.266861584 + -0.2222222222 Combine like terms: 1.266861584 + -0.2222222222 = 1.0446393618 x = 1.0446393618 Simplifying x = 1.0446393618Subproblem 2
x + 0.2222222222 = -1.266861584 Simplifying x + 0.2222222222 = -1.266861584 Reorder the terms: 0.2222222222 + x = -1.266861584 Solving 0.2222222222 + x = -1.266861584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = -1.266861584 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = -1.266861584 + -0.2222222222 x = -1.266861584 + -0.2222222222 Combine like terms: -1.266861584 + -0.2222222222 = -1.4890838062 x = -1.4890838062 Simplifying x = -1.4890838062Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0446393618, -1.4890838062}Solution
x = {0, 1.0446393618, -1.4890838062}
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