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Simplifying 2x3 + -30x2 + 18x = 0 Reorder the terms: 18x + -30x2 + 2x3 = 0 Solving 18x + -30x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(9 + -15x + x2) = 0 Ignore the factor 2.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 '(9 + -15x + x2)' equal to zero and attempt to solve: Simplifying 9 + -15x + x2 = 0 Solving 9 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -15x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -15x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -15x + x2 = 0 + -9 -15x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -15x + x2 = -9 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -9 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -9 + 56.25 Combine like terms: -9 + 56.25 = 47.25 56.25 + -15x + x2 = 47.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 47.25 Calculate the square root of the right side: 6.873863542 Break this problem into two subproblems by setting (x + -7.5) equal to 6.873863542 and -6.873863542.Subproblem 1
x + -7.5 = 6.873863542 Simplifying x + -7.5 = 6.873863542 Reorder the terms: -7.5 + x = 6.873863542 Solving -7.5 + x = 6.873863542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 6.873863542 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 6.873863542 + 7.5 x = 6.873863542 + 7.5 Combine like terms: 6.873863542 + 7.5 = 14.373863542 x = 14.373863542 Simplifying x = 14.373863542Subproblem 2
x + -7.5 = -6.873863542 Simplifying x + -7.5 = -6.873863542 Reorder the terms: -7.5 + x = -6.873863542 Solving -7.5 + x = -6.873863542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -6.873863542 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -6.873863542 + 7.5 x = -6.873863542 + 7.5 Combine like terms: -6.873863542 + 7.5 = 0.626136458 x = 0.626136458 Simplifying x = 0.626136458Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.373863542, 0.626136458}Solution
x = {0, 14.373863542, 0.626136458}
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