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Simplifying 4x6 + 36x5 + 57x4 = 0 Reorder the terms: 57x4 + 36x5 + 4x6 = 0 Solving 57x4 + 36x5 + 4x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x4'. x4(57 + 36x + 4x2) = 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 '(57 + 36x + 4x2)' equal to zero and attempt to solve: Simplifying 57 + 36x + 4x2 = 0 Solving 57 + 36x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 14.25 + 9x + x2 = 0 Move the constant term to the right: Add '-14.25' to each side of the equation. 14.25 + 9x + -14.25 + x2 = 0 + -14.25 Reorder the terms: 14.25 + -14.25 + 9x + x2 = 0 + -14.25 Combine like terms: 14.25 + -14.25 = 0.00 0.00 + 9x + x2 = 0 + -14.25 9x + x2 = 0 + -14.25 Combine like terms: 0 + -14.25 = -14.25 9x + x2 = -14.25 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 = -14.25 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -14.25 + 20.25 Combine like terms: -14.25 + 20.25 = 6 20.25 + 9x + x2 = 6 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + 4.5) equal to 2.449489743 and -2.449489743.Subproblem 1
x + 4.5 = 2.449489743 Simplifying x + 4.5 = 2.449489743 Reorder the terms: 4.5 + x = 2.449489743 Solving 4.5 + x = 2.449489743 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 = 2.449489743 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 2.449489743 + -4.5 x = 2.449489743 + -4.5 Combine like terms: 2.449489743 + -4.5 = -2.050510257 x = -2.050510257 Simplifying x = -2.050510257Subproblem 2
x + 4.5 = -2.449489743 Simplifying x + 4.5 = -2.449489743 Reorder the terms: 4.5 + x = -2.449489743 Solving 4.5 + x = -2.449489743 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 = -2.449489743 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -2.449489743 + -4.5 x = -2.449489743 + -4.5 Combine like terms: -2.449489743 + -4.5 = -6.949489743 x = -6.949489743 Simplifying x = -6.949489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.050510257, -6.949489743}Solution
x = {-2.050510257, -6.949489743}
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