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Simplifying (4x3) + (16x2) + (2x) = 0 Reorder the terms: (2x) + (16x2) + (4x3) = 0 Solving (2x) + (16x2) + (4x3) = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(1 + (8x) + (2x2)) = 0 Ignore the factor 2.Subproblem 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 '(1 + (8x) + (2x2))' equal to zero and attempt to solve: Simplifying 1 + (8x) + (2x2) = 0 Solving 1 + (8x) + (2x2) = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + (4x) + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + (4x) + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + (4x) + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + (4x) + x2 = 0 + -0.5 (4x) + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 (4x) + x2 = -0.5 The x term is (4x). Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. (4x) + 4 + x2 = -0.5 + 4 Reorder the terms: 4 + (4x) + x2 = -0.5 + 4 Combine like terms: -0.5 + 4 = 3.5 4 + (4x) + x2 = 3.5 Factor a perfect square on the left side: ((x) + 2)((x) + 2) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting ((x) + 2) equal to 1.870828693 and -1.870828693.Subproblem 1
(x) + 2 = 1.870828693 Simplifying (x) + 2 = 1.870828693 x + 2 = 1.870828693 Reorder the terms: 2 + x = 1.870828693 Solving 2 + x = 1.870828693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.870828693 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.870828693 + -2 x = 1.870828693 + -2 Combine like terms: 1.870828693 + -2 = -0.129171307 x = -0.129171307 Simplifying x = -0.129171307Subproblem 2
(x) + 2 = -1.870828693 Simplifying (x) + 2 = -1.870828693 x + 2 = -1.870828693 Reorder the terms: 2 + x = -1.870828693 Solving 2 + x = -1.870828693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.870828693 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.870828693 + -2 x = -1.870828693 + -2 Combine like terms: -1.870828693 + -2 = -3.870828693 x = -3.870828693 Simplifying x = -3.870828693Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.129171307, -3.870828693}Solution
x = {0, -0.129171307, -3.870828693}
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