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Simplifying 4x3 + -13x2 + -30x = 0 Reorder the terms: -30x + -13x2 + 4x3 = 0 Solving -30x + -13x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-30 + -13x + 4x2) = 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 + -13x + 4x2)' equal to zero and attempt to solve: Simplifying -30 + -13x + 4x2 = 0 Solving -30 + -13x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7.5 + -3.25x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -3.25x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -3.25x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -3.25x + x2 = 0 + 7.5 -3.25x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -3.25x + x2 = 7.5 The x term is -3.25x. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25x + 2.640625 + x2 = 7.5 + 2.640625 Reorder the terms: 2.640625 + -3.25x + x2 = 7.5 + 2.640625 Combine like terms: 7.5 + 2.640625 = 10.140625 2.640625 + -3.25x + x2 = 10.140625 Factor a perfect square on the left side: (x + -1.625)(x + -1.625) = 10.140625 Calculate the square root of the right side: 3.184434801 Break this problem into two subproblems by setting (x + -1.625) equal to 3.184434801 and -3.184434801.Subproblem 1
x + -1.625 = 3.184434801 Simplifying x + -1.625 = 3.184434801 Reorder the terms: -1.625 + x = 3.184434801 Solving -1.625 + x = 3.184434801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = 3.184434801 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = 3.184434801 + 1.625 x = 3.184434801 + 1.625 Combine like terms: 3.184434801 + 1.625 = 4.809434801 x = 4.809434801 Simplifying x = 4.809434801Subproblem 2
x + -1.625 = -3.184434801 Simplifying x + -1.625 = -3.184434801 Reorder the terms: -1.625 + x = -3.184434801 Solving -1.625 + x = -3.184434801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = -3.184434801 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = -3.184434801 + 1.625 x = -3.184434801 + 1.625 Combine like terms: -3.184434801 + 1.625 = -1.559434801 x = -1.559434801 Simplifying x = -1.559434801Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.809434801, -1.559434801}Solution
x = {0, 4.809434801, -1.559434801}
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