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Simplifying 4x8 + -36x7 + 20x6 = 0 Reorder the terms: 20x6 + -36x7 + 4x8 = 0 Solving 20x6 + -36x7 + 4x8 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x6'. 4x6(5 + -9x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'x6' equal to zero and attempt to solve: Simplifying x6 = 0 Solving x6 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x6 = 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 '(5 + -9x + x2)' equal to zero and attempt to solve: Simplifying 5 + -9x + x2 = 0 Solving 5 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -9x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -9x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -9x + x2 = 0 + -5 -9x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -9x + x2 = -5 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 = -5 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -5 + 20.25 Combine like terms: -5 + 20.25 = 15.25 20.25 + -9x + x2 = 15.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (x + -4.5) equal to 3.905124838 and -3.905124838.Subproblem 1
x + -4.5 = 3.905124838 Simplifying x + -4.5 = 3.905124838 Reorder the terms: -4.5 + x = 3.905124838 Solving -4.5 + x = 3.905124838 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 = 3.905124838 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 3.905124838 + 4.5 x = 3.905124838 + 4.5 Combine like terms: 3.905124838 + 4.5 = 8.405124838 x = 8.405124838 Simplifying x = 8.405124838Subproblem 2
x + -4.5 = -3.905124838 Simplifying x + -4.5 = -3.905124838 Reorder the terms: -4.5 + x = -3.905124838 Solving -4.5 + x = -3.905124838 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 = -3.905124838 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -3.905124838 + 4.5 x = -3.905124838 + 4.5 Combine like terms: -3.905124838 + 4.5 = 0.594875162 x = 0.594875162 Simplifying x = 0.594875162Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.405124838, 0.594875162}Solution
x = {8.405124838, 0.594875162}
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