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Simplifying 6x3 + 24x2 + -2x = 0 Reorder the terms: -2x + 24x2 + 6x3 = 0 Solving -2x + 24x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-1 + 12x + 3x2) = 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 '(-1 + 12x + 3x2)' equal to zero and attempt to solve: Simplifying -1 + 12x + 3x2 = 0 Solving -1 + 12x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.3333333333 + 4x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 4x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 4x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 4x + x2 = 0 + 0.3333333333 4x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 4x + x2 = 0.3333333333 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 0.3333333333 + 4 Reorder the terms: 4 + 4x + x2 = 0.3333333333 + 4 Combine like terms: 0.3333333333 + 4 = 4.3333333333 4 + 4x + x2 = 4.3333333333 Factor a perfect square on the left side: (x + 2)(x + 2) = 4.3333333333 Calculate the square root of the right side: 2.081665999 Break this problem into two subproblems by setting (x + 2) equal to 2.081665999 and -2.081665999.Subproblem 1
x + 2 = 2.081665999 Simplifying x + 2 = 2.081665999 Reorder the terms: 2 + x = 2.081665999 Solving 2 + x = 2.081665999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.081665999 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.081665999 + -2 x = 2.081665999 + -2 Combine like terms: 2.081665999 + -2 = 0.081665999 x = 0.081665999 Simplifying x = 0.081665999Subproblem 2
x + 2 = -2.081665999 Simplifying x + 2 = -2.081665999 Reorder the terms: 2 + x = -2.081665999 Solving 2 + x = -2.081665999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.081665999 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.081665999 + -2 x = -2.081665999 + -2 Combine like terms: -2.081665999 + -2 = -4.081665999 x = -4.081665999 Simplifying x = -4.081665999Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.081665999, -4.081665999}Solution
x = {0, 0.081665999, -4.081665999}
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