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Simplifying 35x3 + -35x2 + 7x = 0 Reorder the terms: 7x + -35x2 + 35x3 = 0 Solving 7x + -35x2 + 35x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7x'. 7x(1 + -5x + 5x2) = 0 Ignore the factor 7.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 + -5x + 5x2)' equal to zero and attempt to solve: Simplifying 1 + -5x + 5x2 = 0 Solving 1 + -5x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + -1x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -1x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -1x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -1x + x2 = 0 + -0.2 -1x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -1x + x2 = -0.2 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -0.2 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.2 + 0.25 Combine like terms: -0.2 + 0.25 = 0.05 0.25 + -1x + x2 = 0.05 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.05 Calculate the square root of the right side: 0.223606798 Break this problem into two subproblems by setting (x + -0.5) equal to 0.223606798 and -0.223606798.Subproblem 1
x + -0.5 = 0.223606798 Simplifying x + -0.5 = 0.223606798 Reorder the terms: -0.5 + x = 0.223606798 Solving -0.5 + x = 0.223606798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.223606798 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.223606798 + 0.5 x = 0.223606798 + 0.5 Combine like terms: 0.223606798 + 0.5 = 0.723606798 x = 0.723606798 Simplifying x = 0.723606798Subproblem 2
x + -0.5 = -0.223606798 Simplifying x + -0.5 = -0.223606798 Reorder the terms: -0.5 + x = -0.223606798 Solving -0.5 + x = -0.223606798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.223606798 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.223606798 + 0.5 x = -0.223606798 + 0.5 Combine like terms: -0.223606798 + 0.5 = 0.276393202 x = 0.276393202 Simplifying x = 0.276393202Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.723606798, 0.276393202}Solution
x = {0, 0.723606798, 0.276393202}
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