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Simplifying -16x5 + -44x4 + 30x3 = 0 Reorder the terms: 30x3 + -44x4 + -16x5 = 0 Solving 30x3 + -44x4 + -16x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x3'. 2x3(15 + -22x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve: Simplifying x3 = 0 Solving x3 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(15 + -22x + -8x2)' equal to zero and attempt to solve: Simplifying 15 + -22x + -8x2 = 0 Solving 15 + -22x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -1.875 + 2.75x + x2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + 2.75x + 1.875 + x2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + 2.75x + x2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + 2.75x + x2 = 0 + 1.875 2.75x + x2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 2.75x + x2 = 1.875 The x term is 2.75x. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75x + 1.890625 + x2 = 1.875 + 1.890625 Reorder the terms: 1.890625 + 2.75x + x2 = 1.875 + 1.890625 Combine like terms: 1.875 + 1.890625 = 3.765625 1.890625 + 2.75x + x2 = 3.765625 Factor a perfect square on the left side: (x + 1.375)(x + 1.375) = 3.765625 Calculate the square root of the right side: 1.940521837 Break this problem into two subproblems by setting (x + 1.375) equal to 1.940521837 and -1.940521837.Subproblem 1
x + 1.375 = 1.940521837 Simplifying x + 1.375 = 1.940521837 Reorder the terms: 1.375 + x = 1.940521837 Solving 1.375 + x = 1.940521837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = 1.940521837 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = 1.940521837 + -1.375 x = 1.940521837 + -1.375 Combine like terms: 1.940521837 + -1.375 = 0.565521837 x = 0.565521837 Simplifying x = 0.565521837Subproblem 2
x + 1.375 = -1.940521837 Simplifying x + 1.375 = -1.940521837 Reorder the terms: 1.375 + x = -1.940521837 Solving 1.375 + x = -1.940521837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = -1.940521837 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = -1.940521837 + -1.375 x = -1.940521837 + -1.375 Combine like terms: -1.940521837 + -1.375 = -3.315521837 x = -3.315521837 Simplifying x = -3.315521837Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.565521837, -3.315521837}Solution
x = {0.565521837, -3.315521837}
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