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Simplifying 12x + 5x2 + -9x3 = 0 Solving 12x + 5x2 + -9x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(12 + 5x + -9x2) = 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 + 5x + -9x2)' equal to zero and attempt to solve: Simplifying 12 + 5x + -9x2 = 0 Solving 12 + 5x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -1.333333333 + -0.5555555556x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -0.5555555556x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -0.5555555556x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -0.5555555556x + x2 = 0 + 1.333333333 -0.5555555556x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -0.5555555556x + x2 = 1.333333333 The x term is -0.5555555556x. Take half its coefficient (-0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. -0.5555555556x + 0.07716049384 + x2 = 1.333333333 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556x + x2 = 1.333333333 + 0.07716049384 Combine like terms: 1.333333333 + 0.07716049384 = 1.41049382684 0.07716049384 + -0.5555555556x + x2 = 1.41049382684 Factor a perfect square on the left side: (x + -0.2777777778)(x + -0.2777777778) = 1.41049382684 Calculate the square root of the right side: 1.187642129 Break this problem into two subproblems by setting (x + -0.2777777778) equal to 1.187642129 and -1.187642129.Subproblem 1
x + -0.2777777778 = 1.187642129 Simplifying x + -0.2777777778 = 1.187642129 Reorder the terms: -0.2777777778 + x = 1.187642129 Solving -0.2777777778 + x = 1.187642129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + x = 1.187642129 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = 1.187642129 + 0.2777777778 x = 1.187642129 + 0.2777777778 Combine like terms: 1.187642129 + 0.2777777778 = 1.4654199068 x = 1.4654199068 Simplifying x = 1.4654199068Subproblem 2
x + -0.2777777778 = -1.187642129 Simplifying x + -0.2777777778 = -1.187642129 Reorder the terms: -0.2777777778 + x = -1.187642129 Solving -0.2777777778 + x = -1.187642129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + x = -1.187642129 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = -1.187642129 + 0.2777777778 x = -1.187642129 + 0.2777777778 Combine like terms: -1.187642129 + 0.2777777778 = -0.9098643512 x = -0.9098643512 Simplifying x = -0.9098643512Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4654199068, -0.9098643512}Solution
x = {0, 1.4654199068, -0.9098643512}
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