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Simplifying 6X4 + -30X3 + 2X2 = 0 Reorder the terms: 2X2 + -30X3 + 6X4 = 0 Solving 2X2 + -30X3 + 6X4 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '2X2'. 2X2(1 + -15X + 3X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'X2' equal to zero and attempt to solve: Simplifying X2 = 0 Solving X2 = 0 Move all terms containing X to the left, all other terms to the right. Simplifying X2 = 0 Take the square root of each side: X = {0}Subproblem 2
Set the factor '(1 + -15X + 3X2)' equal to zero and attempt to solve: Simplifying 1 + -15X + 3X2 = 0 Solving 1 + -15X + 3X2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + -5X + X2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -5X + -0.3333333333 + X2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -5X + X2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -5X + X2 = 0 + -0.3333333333 -5X + X2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -5X + X2 = -0.3333333333 The X term is -5X. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5X + 6.25 + X2 = -0.3333333333 + 6.25 Reorder the terms: 6.25 + -5X + X2 = -0.3333333333 + 6.25 Combine like terms: -0.3333333333 + 6.25 = 5.9166666667 6.25 + -5X + X2 = 5.9166666667 Factor a perfect square on the left side: (X + -2.5)(X + -2.5) = 5.9166666667 Calculate the square root of the right side: 2.43241992 Break this problem into two subproblems by setting (X + -2.5) equal to 2.43241992 and -2.43241992.Subproblem 1
X + -2.5 = 2.43241992 Simplifying X + -2.5 = 2.43241992 Reorder the terms: -2.5 + X = 2.43241992 Solving -2.5 + X = 2.43241992 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + X = 2.43241992 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + X = 2.43241992 + 2.5 X = 2.43241992 + 2.5 Combine like terms: 2.43241992 + 2.5 = 4.93241992 X = 4.93241992 Simplifying X = 4.93241992Subproblem 2
X + -2.5 = -2.43241992 Simplifying X + -2.5 = -2.43241992 Reorder the terms: -2.5 + X = -2.43241992 Solving -2.5 + X = -2.43241992 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + X = -2.43241992 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + X = -2.43241992 + 2.5 X = -2.43241992 + 2.5 Combine like terms: -2.43241992 + 2.5 = 0.06758008 X = 0.06758008 Simplifying X = 0.06758008Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.93241992, 0.06758008}Solution
X = {0, 4.93241992, 0.06758008}
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