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Simplifying x3 + 42x2 + 3x = 0 Reorder the terms: 3x + 42x2 + x3 = 0 Solving 3x + 42x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(3 + 42x + x2) = 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 '(3 + 42x + x2)' equal to zero and attempt to solve: Simplifying 3 + 42x + x2 = 0 Solving 3 + 42x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 42x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 42x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 42x + x2 = 0 + -3 42x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 42x + x2 = -3 The x term is 42x. Take half its coefficient (21). Square it (441) and add it to both sides. Add '441' to each side of the equation. 42x + 441 + x2 = -3 + 441 Reorder the terms: 441 + 42x + x2 = -3 + 441 Combine like terms: -3 + 441 = 438 441 + 42x + x2 = 438 Factor a perfect square on the left side: (x + 21)(x + 21) = 438 Calculate the square root of the right side: 20.928449536 Break this problem into two subproblems by setting (x + 21) equal to 20.928449536 and -20.928449536.Subproblem 1
x + 21 = 20.928449536 Simplifying x + 21 = 20.928449536 Reorder the terms: 21 + x = 20.928449536 Solving 21 + x = 20.928449536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + x = 20.928449536 + -21 Combine like terms: 21 + -21 = 0 0 + x = 20.928449536 + -21 x = 20.928449536 + -21 Combine like terms: 20.928449536 + -21 = -0.071550464 x = -0.071550464 Simplifying x = -0.071550464Subproblem 2
x + 21 = -20.928449536 Simplifying x + 21 = -20.928449536 Reorder the terms: 21 + x = -20.928449536 Solving 21 + x = -20.928449536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + x = -20.928449536 + -21 Combine like terms: 21 + -21 = 0 0 + x = -20.928449536 + -21 x = -20.928449536 + -21 Combine like terms: -20.928449536 + -21 = -41.928449536 x = -41.928449536 Simplifying x = -41.928449536Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.071550464, -41.928449536}Solution
x = {0, -0.071550464, -41.928449536}
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