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Simplifying 4x3 + -20x2 + -25x = 0 Reorder the terms: -25x + -20x2 + 4x3 = 0 Solving -25x + -20x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-25 + -20x + 4x2) = 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 '(-25 + -20x + 4x2)' equal to zero and attempt to solve: Simplifying -25 + -20x + 4x2 = 0 Solving -25 + -20x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.25 + -5x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -5x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -5x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -5x + x2 = 0 + 6.25 -5x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -5x + x2 = 6.25 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 6.25 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 6.25 + 6.25 Combine like terms: 6.25 + 6.25 = 12.5 6.25 + -5x + x2 = 12.5 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (x + -2.5) equal to 3.535533906 and -3.535533906.Subproblem 1
x + -2.5 = 3.535533906 Simplifying x + -2.5 = 3.535533906 Reorder the terms: -2.5 + x = 3.535533906 Solving -2.5 + x = 3.535533906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 3.535533906 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.535533906 + 2.5 x = 3.535533906 + 2.5 Combine like terms: 3.535533906 + 2.5 = 6.035533906 x = 6.035533906 Simplifying x = 6.035533906Subproblem 2
x + -2.5 = -3.535533906 Simplifying x + -2.5 = -3.535533906 Reorder the terms: -2.5 + x = -3.535533906 Solving -2.5 + x = -3.535533906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -3.535533906 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.535533906 + 2.5 x = -3.535533906 + 2.5 Combine like terms: -3.535533906 + 2.5 = -1.035533906 x = -1.035533906 Simplifying x = -1.035533906Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.035533906, -1.035533906}Solution
x = {0, 6.035533906, -1.035533906}
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