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Simplifying x3 + -7x2 + -23x = 0 Reorder the terms: -23x + -7x2 + x3 = 0 Solving -23x + -7x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-23 + -7x + 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 '(-23 + -7x + x2)' equal to zero and attempt to solve: Simplifying -23 + -7x + x2 = 0 Solving -23 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + -7x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + -7x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -7x + x2 = 0 + 23 -7x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 -7x + x2 = 23 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 23 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 23 + 12.25 Combine like terms: 23 + 12.25 = 35.25 12.25 + -7x + x2 = 35.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (x + -3.5) equal to 5.937171044 and -5.937171044.Subproblem 1
x + -3.5 = 5.937171044 Simplifying x + -3.5 = 5.937171044 Reorder the terms: -3.5 + x = 5.937171044 Solving -3.5 + x = 5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 5.937171044 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 5.937171044 + 3.5 x = 5.937171044 + 3.5 Combine like terms: 5.937171044 + 3.5 = 9.437171044 x = 9.437171044 Simplifying x = 9.437171044Subproblem 2
x + -3.5 = -5.937171044 Simplifying x + -3.5 = -5.937171044 Reorder the terms: -3.5 + x = -5.937171044 Solving -3.5 + x = -5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -5.937171044 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -5.937171044 + 3.5 x = -5.937171044 + 3.5 Combine like terms: -5.937171044 + 3.5 = -2.437171044 x = -2.437171044 Simplifying x = -2.437171044Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.437171044, -2.437171044}Solution
x = {0, 9.437171044, -2.437171044}
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