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Simplifying 0 = 4x3 + 3x2 + -12x Reorder the terms: 0 = -12x + 3x2 + 4x3 Solving 0 = -12x + 3x2 + 4x3 Solving for variable 'x'. Remove the zero: 12x + -3x2 + -4x3 = -12x + 3x2 + 4x3 + 12x + -3x2 + -4x3 Reorder the terms: 12x + -3x2 + -4x3 = -12x + 12x + 3x2 + -3x2 + 4x3 + -4x3 Combine like terms: -12x + 12x = 0 12x + -3x2 + -4x3 = 0 + 3x2 + -3x2 + 4x3 + -4x3 12x + -3x2 + -4x3 = 3x2 + -3x2 + 4x3 + -4x3 Combine like terms: 3x2 + -3x2 = 0 12x + -3x2 + -4x3 = 0 + 4x3 + -4x3 12x + -3x2 + -4x3 = 4x3 + -4x3 Combine like terms: 4x3 + -4x3 = 0 12x + -3x2 + -4x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(12 + -3x + -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 + -3x + -4x2)' equal to zero and attempt to solve: Simplifying 12 + -3x + -4x2 = 0 Solving 12 + -3x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -3 + 0.75x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 0.75x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 0.75x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 0.75x + x2 = 0 + 3 0.75x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 0.75x + x2 = 3 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 3 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 3 + 0.140625 Combine like terms: 3 + 0.140625 = 3.140625 0.140625 + 0.75x + x2 = 3.140625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 3.140625 Calculate the square root of the right side: 1.77218086 Break this problem into two subproblems by setting (x + 0.375) equal to 1.77218086 and -1.77218086.Subproblem 1
x + 0.375 = 1.77218086 Simplifying x + 0.375 = 1.77218086 Reorder the terms: 0.375 + x = 1.77218086 Solving 0.375 + x = 1.77218086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 1.77218086 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 1.77218086 + -0.375 x = 1.77218086 + -0.375 Combine like terms: 1.77218086 + -0.375 = 1.39718086 x = 1.39718086 Simplifying x = 1.39718086Subproblem 2
x + 0.375 = -1.77218086 Simplifying x + 0.375 = -1.77218086 Reorder the terms: 0.375 + x = -1.77218086 Solving 0.375 + x = -1.77218086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -1.77218086 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -1.77218086 + -0.375 x = -1.77218086 + -0.375 Combine like terms: -1.77218086 + -0.375 = -2.14718086 x = -2.14718086 Simplifying x = -2.14718086Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.39718086, -2.14718086}Solution
x = {0, 1.39718086, -2.14718086}
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