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Simplifying 2x3 + 17x2 + 9x = 0 Reorder the terms: 9x + 17x2 + 2x3 = 0 Solving 9x + 17x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(9 + 17x + 2x2) = 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 '(9 + 17x + 2x2)' equal to zero and attempt to solve: Simplifying 9 + 17x + 2x2 = 0 Solving 9 + 17x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + 8.5x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + 8.5x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + 8.5x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + 8.5x + x2 = 0 + -4.5 8.5x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 8.5x + x2 = -4.5 The x term is 8.5x. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5x + 18.0625 + x2 = -4.5 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = -4.5 + 18.0625 Combine like terms: -4.5 + 18.0625 = 13.5625 18.0625 + 8.5x + x2 = 13.5625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 13.5625 Calculate the square root of the right side: 3.682729966 Break this problem into two subproblems by setting (x + 4.25) equal to 3.682729966 and -3.682729966.Subproblem 1
x + 4.25 = 3.682729966 Simplifying x + 4.25 = 3.682729966 Reorder the terms: 4.25 + x = 3.682729966 Solving 4.25 + x = 3.682729966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 3.682729966 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 3.682729966 + -4.25 x = 3.682729966 + -4.25 Combine like terms: 3.682729966 + -4.25 = -0.567270034 x = -0.567270034 Simplifying x = -0.567270034Subproblem 2
x + 4.25 = -3.682729966 Simplifying x + 4.25 = -3.682729966 Reorder the terms: 4.25 + x = -3.682729966 Solving 4.25 + x = -3.682729966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -3.682729966 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -3.682729966 + -4.25 x = -3.682729966 + -4.25 Combine like terms: -3.682729966 + -4.25 = -7.932729966 x = -7.932729966 Simplifying x = -7.932729966Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.567270034, -7.932729966}Solution
x = {0, -0.567270034, -7.932729966}
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