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Simplifying x3 + 35x2 + x = 0 Reorder the terms: x + 35x2 + x3 = 0 Solving x + 35x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(1 + 35x + 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 '(1 + 35x + x2)' equal to zero and attempt to solve: Simplifying 1 + 35x + x2 = 0 Solving 1 + 35x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 35x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 35x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 35x + x2 = 0 + -1 35x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 35x + x2 = -1 The x term is 35x. Take half its coefficient (17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. 35x + 306.25 + x2 = -1 + 306.25 Reorder the terms: 306.25 + 35x + x2 = -1 + 306.25 Combine like terms: -1 + 306.25 = 305.25 306.25 + 35x + x2 = 305.25 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 305.25 Calculate the square root of the right side: 17.47140521 Break this problem into two subproblems by setting (x + 17.5) equal to 17.47140521 and -17.47140521.Subproblem 1
x + 17.5 = 17.47140521 Simplifying x + 17.5 = 17.47140521 Reorder the terms: 17.5 + x = 17.47140521 Solving 17.5 + x = 17.47140521 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = 17.47140521 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 17.47140521 + -17.5 x = 17.47140521 + -17.5 Combine like terms: 17.47140521 + -17.5 = -0.02859479 x = -0.02859479 Simplifying x = -0.02859479Subproblem 2
x + 17.5 = -17.47140521 Simplifying x + 17.5 = -17.47140521 Reorder the terms: 17.5 + x = -17.47140521 Solving 17.5 + x = -17.47140521 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = -17.47140521 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -17.47140521 + -17.5 x = -17.47140521 + -17.5 Combine like terms: -17.47140521 + -17.5 = -34.97140521 x = -34.97140521 Simplifying x = -34.97140521Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.02859479, -34.97140521}Solution
x = {0, -0.02859479, -34.97140521}
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