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Simplifying 9x + -15x2 + -27x3 = 0 Solving 9x + -15x2 + -27x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(3 + -5x + -9x2) = 0 Ignore the factor 3.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 '(3 + -5x + -9x2)' equal to zero and attempt to solve: Simplifying 3 + -5x + -9x2 = 0 Solving 3 + -5x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.3333333333 + 0.5555555556x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 0.5555555556x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 0.5555555556x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 0.5555555556x + x2 = 0 + 0.3333333333 0.5555555556x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 0.5555555556x + x2 = 0.3333333333 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 = 0.3333333333 + 0.07716049384 Reorder the terms: 0.07716049384 + 0.5555555556x + x2 = 0.3333333333 + 0.07716049384 Combine like terms: 0.3333333333 + 0.07716049384 = 0.41049382714 0.07716049384 + 0.5555555556x + x2 = 0.41049382714 Factor a perfect square on the left side: (x + 0.2777777778)(x + 0.2777777778) = 0.41049382714 Calculate the square root of the right side: 0.640697922 Break this problem into two subproblems by setting (x + 0.2777777778) equal to 0.640697922 and -0.640697922.Subproblem 1
x + 0.2777777778 = 0.640697922 Simplifying x + 0.2777777778 = 0.640697922 Reorder the terms: 0.2777777778 + x = 0.640697922 Solving 0.2777777778 + x = 0.640697922 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 = 0.640697922 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = 0.640697922 + -0.2777777778 x = 0.640697922 + -0.2777777778 Combine like terms: 0.640697922 + -0.2777777778 = 0.3629201442 x = 0.3629201442 Simplifying x = 0.3629201442Subproblem 2
x + 0.2777777778 = -0.640697922 Simplifying x + 0.2777777778 = -0.640697922 Reorder the terms: 0.2777777778 + x = -0.640697922 Solving 0.2777777778 + x = -0.640697922 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 = -0.640697922 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = -0.640697922 + -0.2777777778 x = -0.640697922 + -0.2777777778 Combine like terms: -0.640697922 + -0.2777777778 = -0.9184756998 x = -0.9184756998 Simplifying x = -0.9184756998Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3629201442, -0.9184756998}Solution
x = {0, 0.3629201442, -0.9184756998}
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