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Simplifying 3x(2 + -1x) = x(3x + -2) + -24 (2 * 3x + -1x * 3x) = x(3x + -2) + -24 (6x + -3x2) = x(3x + -2) + -24 Reorder the terms: 6x + -3x2 = x(-2 + 3x) + -24 6x + -3x2 = (-2 * x + 3x * x) + -24 6x + -3x2 = (-2x + 3x2) + -24 Reorder the terms: 6x + -3x2 = -24 + -2x + 3x2 Solving 6x + -3x2 = -24 + -2x + 3x2 Solving for variable 'x'. Reorder the terms: 24 + 6x + 2x + -3x2 + -3x2 = -24 + -2x + 3x2 + 24 + 2x + -3x2 Combine like terms: 6x + 2x = 8x 24 + 8x + -3x2 + -3x2 = -24 + -2x + 3x2 + 24 + 2x + -3x2 Combine like terms: -3x2 + -3x2 = -6x2 24 + 8x + -6x2 = -24 + -2x + 3x2 + 24 + 2x + -3x2 Reorder the terms: 24 + 8x + -6x2 = -24 + 24 + -2x + 2x + 3x2 + -3x2 Combine like terms: -24 + 24 = 0 24 + 8x + -6x2 = 0 + -2x + 2x + 3x2 + -3x2 24 + 8x + -6x2 = -2x + 2x + 3x2 + -3x2 Combine like terms: -2x + 2x = 0 24 + 8x + -6x2 = 0 + 3x2 + -3x2 24 + 8x + -6x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 24 + 8x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 4x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + 4x + -3x2)' equal to zero and attempt to solve: Simplifying 12 + 4x + -3x2 = 0 Solving 12 + 4x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -4 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -1.333333333x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -1.333333333x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1.333333333x + x2 = 0 + 4 -1.333333333x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1.333333333x + x2 = 4 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = 4 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 4 + 0.4444444442 Combine like terms: 4 + 0.4444444442 = 4.4444444442 0.4444444442 + -1.333333333x + x2 = 4.4444444442 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 4.4444444442 Calculate the square root of the right side: 2.108185107 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 2.108185107 and -2.108185107.Subproblem 1
x + -0.6666666665 = 2.108185107 Simplifying x + -0.6666666665 = 2.108185107 Reorder the terms: -0.6666666665 + x = 2.108185107 Solving -0.6666666665 + x = 2.108185107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 2.108185107 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 2.108185107 + 0.6666666665 x = 2.108185107 + 0.6666666665 Combine like terms: 2.108185107 + 0.6666666665 = 2.7748517735 x = 2.7748517735 Simplifying x = 2.7748517735Subproblem 2
x + -0.6666666665 = -2.108185107 Simplifying x + -0.6666666665 = -2.108185107 Reorder the terms: -0.6666666665 + x = -2.108185107 Solving -0.6666666665 + x = -2.108185107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -2.108185107 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -2.108185107 + 0.6666666665 x = -2.108185107 + 0.6666666665 Combine like terms: -2.108185107 + 0.6666666665 = -1.4415184405 x = -1.4415184405 Simplifying x = -1.4415184405Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.7748517735, -1.4415184405}Solution
x = {2.7748517735, -1.4415184405}
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