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Simplifying 4x(3x2 + -2x + 3) + -6[3x + -1x(2x + -5)] = 0 Reorder the terms: 4x(3 + -2x + 3x2) + -6[3x + -1x(2x + -5)] = 0 (3 * 4x + -2x * 4x + 3x2 * 4x) + -6[3x + -1x(2x + -5)] = 0 (12x + -8x2 + 12x3) + -6[3x + -1x(2x + -5)] = 0 Reorder the terms: 12x + -8x2 + 12x3 + -6[3x + -1x(-5 + 2x)] = 0 12x + -8x2 + 12x3 + -6[3x + (-5 * -1x + 2x * -1x)] = 0 12x + -8x2 + 12x3 + -6[3x + (5x + -2x2)] = 0 Combine like terms: 3x + 5x = 8x 12x + -8x2 + 12x3 + -6[8x + -2x2] = 0 12x + -8x2 + 12x3 + [8x * -6 + -2x2 * -6] = 0 12x + -8x2 + 12x3 + [-48x + 12x2] = 0 Reorder the terms: 12x + -48x + -8x2 + 12x2 + 12x3 = 0 Combine like terms: 12x + -48x = -36x -36x + -8x2 + 12x2 + 12x3 = 0 Combine like terms: -8x2 + 12x2 = 4x2 -36x + 4x2 + 12x3 = 0 Solving -36x + 4x2 + 12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(-9 + x + 3x2) = 0 Ignore the factor 4.Subproblem 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 '(-9 + x + 3x2)' equal to zero and attempt to solve: Simplifying -9 + x + 3x2 = 0 Solving -9 + x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 0.3333333333x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 0.3333333333x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 0.3333333333x + x2 = 0 + 3 0.3333333333x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 0.3333333333x + x2 = 3 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333x + 0.25 + x2 = 3 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = 3 + 0.25 Combine like terms: 3 + 0.25 = 3.25 0.25 + 0.3333333333x + x2 = 3.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (x + 0.5) equal to 1.802775638 and -1.802775638.Subproblem 1
x + 0.5 = 1.802775638 Simplifying x + 0.5 = 1.802775638 Reorder the terms: 0.5 + x = 1.802775638 Solving 0.5 + x = 1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.802775638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.802775638 + -0.5 x = 1.802775638 + -0.5 Combine like terms: 1.802775638 + -0.5 = 1.302775638 x = 1.302775638 Simplifying x = 1.302775638Subproblem 2
x + 0.5 = -1.802775638 Simplifying x + 0.5 = -1.802775638 Reorder the terms: 0.5 + x = -1.802775638 Solving 0.5 + x = -1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.802775638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.802775638 + -0.5 x = -1.802775638 + -0.5 Combine like terms: -1.802775638 + -0.5 = -2.302775638 x = -2.302775638 Simplifying x = -2.302775638Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.302775638, -2.302775638}Solution
x = {0, 1.302775638, -2.302775638}
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