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Simplifying 16x3 + 117x2 + -30x = 0 Reorder the terms: -30x + 117x2 + 16x3 = 0 Solving -30x + 117x2 + 16x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-30 + 117x + 16x2) = 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 + 117x + 16x2)' equal to zero and attempt to solve: Simplifying -30 + 117x + 16x2 = 0 Solving -30 + 117x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.875 + 7.3125x + x2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + 7.3125x + 1.875 + x2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + 7.3125x + x2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + 7.3125x + x2 = 0 + 1.875 7.3125x + x2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 7.3125x + x2 = 1.875 The x term is 7.3125x. Take half its coefficient (3.65625). Square it (13.36816406) and add it to both sides. Add '13.36816406' to each side of the equation. 7.3125x + 13.36816406 + x2 = 1.875 + 13.36816406 Reorder the terms: 13.36816406 + 7.3125x + x2 = 1.875 + 13.36816406 Combine like terms: 1.875 + 13.36816406 = 15.24316406 13.36816406 + 7.3125x + x2 = 15.24316406 Factor a perfect square on the left side: (x + 3.65625)(x + 3.65625) = 15.24316406 Calculate the square root of the right side: 3.904249487 Break this problem into two subproblems by setting (x + 3.65625) equal to 3.904249487 and -3.904249487.Subproblem 1
x + 3.65625 = 3.904249487 Simplifying x + 3.65625 = 3.904249487 Reorder the terms: 3.65625 + x = 3.904249487 Solving 3.65625 + x = 3.904249487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.65625' to each side of the equation. 3.65625 + -3.65625 + x = 3.904249487 + -3.65625 Combine like terms: 3.65625 + -3.65625 = 0.00000 0.00000 + x = 3.904249487 + -3.65625 x = 3.904249487 + -3.65625 Combine like terms: 3.904249487 + -3.65625 = 0.247999487 x = 0.247999487 Simplifying x = 0.247999487Subproblem 2
x + 3.65625 = -3.904249487 Simplifying x + 3.65625 = -3.904249487 Reorder the terms: 3.65625 + x = -3.904249487 Solving 3.65625 + x = -3.904249487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.65625' to each side of the equation. 3.65625 + -3.65625 + x = -3.904249487 + -3.65625 Combine like terms: 3.65625 + -3.65625 = 0.00000 0.00000 + x = -3.904249487 + -3.65625 x = -3.904249487 + -3.65625 Combine like terms: -3.904249487 + -3.65625 = -7.560499487 x = -7.560499487 Simplifying x = -7.560499487Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.247999487, -7.560499487}Solution
x = {0, 0.247999487, -7.560499487}
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