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Simplifying x6 + -9x5 + -30x4 = 0 Reorder the terms: -30x4 + -9x5 + x6 = 0 Solving -30x4 + -9x5 + x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x4'. x4(-30 + -9x + x2) = 0Subproblem 1
Set the factor 'x4' equal to zero and attempt to solve: Simplifying x4 = 0 Solving x4 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-30 + -9x + x2)' equal to zero and attempt to solve: Simplifying -30 + -9x + x2 = 0 Solving -30 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + -9x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -9x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -9x + x2 = 0 + 30 -9x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -9x + x2 = 30 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 30 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 30 + 20.25 Combine like terms: 30 + 20.25 = 50.25 20.25 + -9x + x2 = 50.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (x + -4.5) equal to 7.088723439 and -7.088723439.Subproblem 1
x + -4.5 = 7.088723439 Simplifying x + -4.5 = 7.088723439 Reorder the terms: -4.5 + x = 7.088723439 Solving -4.5 + x = 7.088723439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 7.088723439 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 7.088723439 + 4.5 x = 7.088723439 + 4.5 Combine like terms: 7.088723439 + 4.5 = 11.588723439 x = 11.588723439 Simplifying x = 11.588723439Subproblem 2
x + -4.5 = -7.088723439 Simplifying x + -4.5 = -7.088723439 Reorder the terms: -4.5 + x = -7.088723439 Solving -4.5 + x = -7.088723439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -7.088723439 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -7.088723439 + 4.5 x = -7.088723439 + 4.5 Combine like terms: -7.088723439 + 4.5 = -2.588723439 x = -2.588723439 Simplifying x = -2.588723439Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.588723439, -2.588723439}Solution
x = {11.588723439, -2.588723439}
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