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Simplifying x3 + -19x2 + -30x = 0 Reorder the terms: -30x + -19x2 + x3 = 0 Solving -30x + -19x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-30 + -19x + x2) = 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 '(-30 + -19x + x2)' equal to zero and attempt to solve: Simplifying -30 + -19x + x2 = 0 Solving -30 + -19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + -19x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -19x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -19x + x2 = 0 + 30 -19x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -19x + x2 = 30 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = 30 + 90.25 Reorder the terms: 90.25 + -19x + x2 = 30 + 90.25 Combine like terms: 30 + 90.25 = 120.25 90.25 + -19x + x2 = 120.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 120.25 Calculate the square root of the right side: 10.9658561 Break this problem into two subproblems by setting (x + -9.5) equal to 10.9658561 and -10.9658561.Subproblem 1
x + -9.5 = 10.9658561 Simplifying x + -9.5 = 10.9658561 Reorder the terms: -9.5 + x = 10.9658561 Solving -9.5 + x = 10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 10.9658561 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 10.9658561 + 9.5 x = 10.9658561 + 9.5 Combine like terms: 10.9658561 + 9.5 = 20.4658561 x = 20.4658561 Simplifying x = 20.4658561Subproblem 2
x + -9.5 = -10.9658561 Simplifying x + -9.5 = -10.9658561 Reorder the terms: -9.5 + x = -10.9658561 Solving -9.5 + x = -10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -10.9658561 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -10.9658561 + 9.5 x = -10.9658561 + 9.5 Combine like terms: -10.9658561 + 9.5 = -1.4658561 x = -1.4658561 Simplifying x = -1.4658561Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.4658561, -1.4658561}Solution
x = {0, 20.4658561, -1.4658561}
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