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Simplifying 0 = 2x3 + -4x2 + -12x Reorder the terms: 0 = -12x + -4x2 + 2x3 Solving 0 = -12x + -4x2 + 2x3 Solving for variable 'x'. Remove the zero: 12x + 4x2 + -2x3 = -12x + -4x2 + 2x3 + 12x + 4x2 + -2x3 Reorder the terms: 12x + 4x2 + -2x3 = -12x + 12x + -4x2 + 4x2 + 2x3 + -2x3 Combine like terms: -12x + 12x = 0 12x + 4x2 + -2x3 = 0 + -4x2 + 4x2 + 2x3 + -2x3 12x + 4x2 + -2x3 = -4x2 + 4x2 + 2x3 + -2x3 Combine like terms: -4x2 + 4x2 = 0 12x + 4x2 + -2x3 = 0 + 2x3 + -2x3 12x + 4x2 + -2x3 = 2x3 + -2x3 Combine like terms: 2x3 + -2x3 = 0 12x + 4x2 + -2x3 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(6 + 2x + -1x2) = 0 Ignore the factor 2.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 '(6 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying 6 + 2x + -1x2 = 0 Solving 6 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -6 + -2x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -2x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -2x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -2x + x2 = 0 + 6 -2x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -2x + x2 = 6 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 6 + 1 Reorder the terms: 1 + -2x + x2 = 6 + 1 Combine like terms: 6 + 1 = 7 1 + -2x + x2 = 7 Factor a perfect square on the left side: (x + -1)(x + -1) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + -1) equal to 2.645751311 and -2.645751311.Subproblem 1
x + -1 = 2.645751311 Simplifying x + -1 = 2.645751311 Reorder the terms: -1 + x = 2.645751311 Solving -1 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.645751311 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.645751311 + 1 x = 2.645751311 + 1 Combine like terms: 2.645751311 + 1 = 3.645751311 x = 3.645751311 Simplifying x = 3.645751311Subproblem 2
x + -1 = -2.645751311 Simplifying x + -1 = -2.645751311 Reorder the terms: -1 + x = -2.645751311 Solving -1 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.645751311 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.645751311 + 1 x = -2.645751311 + 1 Combine like terms: -2.645751311 + 1 = -1.645751311 x = -1.645751311 Simplifying x = -1.645751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.645751311, -1.645751311}Solution
x = {0, 3.645751311, -1.645751311}
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