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Simplifying 2x3 + 54x2 + -7x = 0 Reorder the terms: -7x + 54x2 + 2x3 = 0 Solving -7x + 54x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-7 + 54x + 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 '(-7 + 54x + 2x2)' equal to zero and attempt to solve: Simplifying -7 + 54x + 2x2 = 0 Solving -7 + 54x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 27x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 27x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 27x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 27x + x2 = 0 + 3.5 27x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 27x + x2 = 3.5 The x term is 27x. Take half its coefficient (13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. 27x + 182.25 + x2 = 3.5 + 182.25 Reorder the terms: 182.25 + 27x + x2 = 3.5 + 182.25 Combine like terms: 3.5 + 182.25 = 185.75 182.25 + 27x + x2 = 185.75 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 185.75 Calculate the square root of the right side: 13.62901317 Break this problem into two subproblems by setting (x + 13.5) equal to 13.62901317 and -13.62901317.Subproblem 1
x + 13.5 = 13.62901317 Simplifying x + 13.5 = 13.62901317 Reorder the terms: 13.5 + x = 13.62901317 Solving 13.5 + x = 13.62901317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = 13.62901317 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 13.62901317 + -13.5 x = 13.62901317 + -13.5 Combine like terms: 13.62901317 + -13.5 = 0.12901317 x = 0.12901317 Simplifying x = 0.12901317Subproblem 2
x + 13.5 = -13.62901317 Simplifying x + 13.5 = -13.62901317 Reorder the terms: 13.5 + x = -13.62901317 Solving 13.5 + x = -13.62901317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = -13.62901317 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -13.62901317 + -13.5 x = -13.62901317 + -13.5 Combine like terms: -13.62901317 + -13.5 = -27.12901317 x = -27.12901317 Simplifying x = -27.12901317Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.12901317, -27.12901317}Solution
x = {0, 0.12901317, -27.12901317}
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