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Simplifying 6x8 + -54x7 + 24x6 = 0 Reorder the terms: 24x6 + -54x7 + 6x8 = 0 Solving 24x6 + -54x7 + 6x8 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x6'. 6x6(4 + -9x + x2) = 0 Ignore the factor 6.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 '(4 + -9x + x2)' equal to zero and attempt to solve: Simplifying 4 + -9x + x2 = 0 Solving 4 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -9x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -9x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -9x + x2 = 0 + -4 -9x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -9x + x2 = -4 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 = -4 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -4 + 20.25 Combine like terms: -4 + 20.25 = 16.25 20.25 + -9x + x2 = 16.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (x + -4.5) equal to 4.031128874 and -4.031128874.Subproblem 1
x + -4.5 = 4.031128874 Simplifying x + -4.5 = 4.031128874 Reorder the terms: -4.5 + x = 4.031128874 Solving -4.5 + x = 4.031128874 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 = 4.031128874 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 4.031128874 + 4.5 x = 4.031128874 + 4.5 Combine like terms: 4.031128874 + 4.5 = 8.531128874 x = 8.531128874 Simplifying x = 8.531128874Subproblem 2
x + -4.5 = -4.031128874 Simplifying x + -4.5 = -4.031128874 Reorder the terms: -4.5 + x = -4.031128874 Solving -4.5 + x = -4.031128874 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 = -4.031128874 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -4.031128874 + 4.5 x = -4.031128874 + 4.5 Combine like terms: -4.031128874 + 4.5 = 0.468871126 x = 0.468871126 Simplifying x = 0.468871126Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.531128874, 0.468871126}Solution
x = {8.531128874, 0.468871126}
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