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Simplifying x4 + -5x3 + -3x2 = 0 Reorder the terms: -3x2 + -5x3 + x4 = 0 Solving -3x2 + -5x3 + x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-3 + -5x + x2) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-3 + -5x + x2)' equal to zero and attempt to solve: Simplifying -3 + -5x + x2 = 0 Solving -3 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -5x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -5x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5x + x2 = 0 + 3 -5x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -5x + x2 = 3 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 = 3 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 3 + 6.25 Combine like terms: 3 + 6.25 = 9.25 6.25 + -5x + x2 = 9.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (x + -2.5) equal to 3.041381265 and -3.041381265.Subproblem 1
x + -2.5 = 3.041381265 Simplifying x + -2.5 = 3.041381265 Reorder the terms: -2.5 + x = 3.041381265 Solving -2.5 + x = 3.041381265 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 = 3.041381265 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.041381265 + 2.5 x = 3.041381265 + 2.5 Combine like terms: 3.041381265 + 2.5 = 5.541381265 x = 5.541381265 Simplifying x = 5.541381265Subproblem 2
x + -2.5 = -3.041381265 Simplifying x + -2.5 = -3.041381265 Reorder the terms: -2.5 + x = -3.041381265 Solving -2.5 + x = -3.041381265 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 = -3.041381265 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.041381265 + 2.5 x = -3.041381265 + 2.5 Combine like terms: -3.041381265 + 2.5 = -0.541381265 x = -0.541381265 Simplifying x = -0.541381265Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.541381265, -0.541381265}Solution
x = {0, 5.541381265, -0.541381265}
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