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Simplifying 25x3 + -75x2 + -1x = 0 Reorder the terms: -1x + -75x2 + 25x3 = 0 Solving -1x + -75x2 + 25x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-1 + -75x + 25x2) = 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 + -75x + 25x2)' equal to zero and attempt to solve: Simplifying -1 + -75x + 25x2 = 0 Solving -1 + -75x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.04 + -3x + x2 = 0 Move the constant term to the right: Add '0.04' to each side of the equation. -0.04 + -3x + 0.04 + x2 = 0 + 0.04 Reorder the terms: -0.04 + 0.04 + -3x + x2 = 0 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.00 + -3x + x2 = 0 + 0.04 -3x + x2 = 0 + 0.04 Combine like terms: 0 + 0.04 = 0.04 -3x + x2 = 0.04 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 0.04 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 0.04 + 2.25 Combine like terms: 0.04 + 2.25 = 2.29 2.25 + -3x + x2 = 2.29 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 2.29 Calculate the square root of the right side: 1.513274595 Break this problem into two subproblems by setting (x + -1.5) equal to 1.513274595 and -1.513274595.Subproblem 1
x + -1.5 = 1.513274595 Simplifying x + -1.5 = 1.513274595 Reorder the terms: -1.5 + x = 1.513274595 Solving -1.5 + x = 1.513274595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.513274595 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.513274595 + 1.5 x = 1.513274595 + 1.5 Combine like terms: 1.513274595 + 1.5 = 3.013274595 x = 3.013274595 Simplifying x = 3.013274595Subproblem 2
x + -1.5 = -1.513274595 Simplifying x + -1.5 = -1.513274595 Reorder the terms: -1.5 + x = -1.513274595 Solving -1.5 + x = -1.513274595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.513274595 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.513274595 + 1.5 x = -1.513274595 + 1.5 Combine like terms: -1.513274595 + 1.5 = -0.013274595 x = -0.013274595 Simplifying x = -0.013274595Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.013274595, -0.013274595}Solution
x = {0, 3.013274595, -0.013274595}
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