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Simplifying x2 + 3x3 + x(4 + -4x) = 233x x2 + 3x3 + (4 * x + -4x * x) = 233x x2 + 3x3 + (4x + -4x2) = 233x Reorder the terms: 4x + x2 + -4x2 + 3x3 = 233x Combine like terms: x2 + -4x2 = -3x2 4x + -3x2 + 3x3 = 233x Solving 4x + -3x2 + 3x3 = 233x Solving for variable 'x'. Reorder the terms: 4x + -233x + -3x2 + 3x3 = 233x + -233x Combine like terms: 4x + -233x = -229x -229x + -3x2 + 3x3 = 233x + -233x Combine like terms: 233x + -233x = 0 -229x + -3x2 + 3x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-229 + -3x + 3x2) = 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 '(-229 + -3x + 3x2)' equal to zero and attempt to solve: Simplifying -229 + -3x + 3x2 = 0 Solving -229 + -3x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -76.33333333 + -1x + x2 = 0 Move the constant term to the right: Add '76.33333333' to each side of the equation. -76.33333333 + -1x + 76.33333333 + x2 = 0 + 76.33333333 Reorder the terms: -76.33333333 + 76.33333333 + -1x + x2 = 0 + 76.33333333 Combine like terms: -76.33333333 + 76.33333333 = 0.00000000 0.00000000 + -1x + x2 = 0 + 76.33333333 -1x + x2 = 0 + 76.33333333 Combine like terms: 0 + 76.33333333 = 76.33333333 -1x + x2 = 76.33333333 The x term is -1x. 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. -1x + 0.25 + x2 = 76.33333333 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 76.33333333 + 0.25 Combine like terms: 76.33333333 + 0.25 = 76.58333333 0.25 + -1x + x2 = 76.58333333 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 76.58333333 Calculate the square root of the right side: 8.751190395 Break this problem into two subproblems by setting (x + -0.5) equal to 8.751190395 and -8.751190395.Subproblem 1
x + -0.5 = 8.751190395 Simplifying x + -0.5 = 8.751190395 Reorder the terms: -0.5 + x = 8.751190395 Solving -0.5 + x = 8.751190395 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 = 8.751190395 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 8.751190395 + 0.5 x = 8.751190395 + 0.5 Combine like terms: 8.751190395 + 0.5 = 9.251190395 x = 9.251190395 Simplifying x = 9.251190395Subproblem 2
x + -0.5 = -8.751190395 Simplifying x + -0.5 = -8.751190395 Reorder the terms: -0.5 + x = -8.751190395 Solving -0.5 + x = -8.751190395 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 = -8.751190395 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -8.751190395 + 0.5 x = -8.751190395 + 0.5 Combine like terms: -8.751190395 + 0.5 = -8.251190395 x = -8.251190395 Simplifying x = -8.251190395Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.251190395, -8.251190395}Solution
x = {0, 9.251190395, -8.251190395}
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