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Simplifying 5x3 + -18x2 + -18x = 0 Reorder the terms: -18x + -18x2 + 5x3 = 0 Solving -18x + -18x2 + 5x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-18 + -18x + 5x2) = 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 '(-18 + -18x + 5x2)' equal to zero and attempt to solve: Simplifying -18 + -18x + 5x2 = 0 Solving -18 + -18x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.6 + -3.6x + x2 = 0 Move the constant term to the right: Add '3.6' to each side of the equation. -3.6 + -3.6x + 3.6 + x2 = 0 + 3.6 Reorder the terms: -3.6 + 3.6 + -3.6x + x2 = 0 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + -3.6x + x2 = 0 + 3.6 -3.6x + x2 = 0 + 3.6 Combine like terms: 0 + 3.6 = 3.6 -3.6x + x2 = 3.6 The x term is -3.6x. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6x + 3.24 + x2 = 3.6 + 3.24 Reorder the terms: 3.24 + -3.6x + x2 = 3.6 + 3.24 Combine like terms: 3.6 + 3.24 = 6.84 3.24 + -3.6x + x2 = 6.84 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 6.84 Calculate the square root of the right side: 2.615339366 Break this problem into two subproblems by setting (x + -1.8) equal to 2.615339366 and -2.615339366.Subproblem 1
x + -1.8 = 2.615339366 Simplifying x + -1.8 = 2.615339366 Reorder the terms: -1.8 + x = 2.615339366 Solving -1.8 + x = 2.615339366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = 2.615339366 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 2.615339366 + 1.8 x = 2.615339366 + 1.8 Combine like terms: 2.615339366 + 1.8 = 4.415339366 x = 4.415339366 Simplifying x = 4.415339366Subproblem 2
x + -1.8 = -2.615339366 Simplifying x + -1.8 = -2.615339366 Reorder the terms: -1.8 + x = -2.615339366 Solving -1.8 + x = -2.615339366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = -2.615339366 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -2.615339366 + 1.8 x = -2.615339366 + 1.8 Combine like terms: -2.615339366 + 1.8 = -0.815339366 x = -0.815339366 Simplifying x = -0.815339366Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.415339366, -0.815339366}Solution
x = {0, 4.415339366, -0.815339366}
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