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Simplifying 3x5 + -111x4 + 27x3 = 0 Reorder the terms: 27x3 + -111x4 + 3x5 = 0 Solving 27x3 + -111x4 + 3x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x3'. 3x3(9 + -37x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve: Simplifying x3 = 0 Solving x3 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3 = 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 '(9 + -37x + x2)' equal to zero and attempt to solve: Simplifying 9 + -37x + x2 = 0 Solving 9 + -37x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -37x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -37x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -37x + x2 = 0 + -9 -37x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -37x + x2 = -9 The x term is -37x. Take half its coefficient (-18.5). Square it (342.25) and add it to both sides. Add '342.25' to each side of the equation. -37x + 342.25 + x2 = -9 + 342.25 Reorder the terms: 342.25 + -37x + x2 = -9 + 342.25 Combine like terms: -9 + 342.25 = 333.25 342.25 + -37x + x2 = 333.25 Factor a perfect square on the left side: (x + -18.5)(x + -18.5) = 333.25 Calculate the square root of the right side: 18.255136264 Break this problem into two subproblems by setting (x + -18.5) equal to 18.255136264 and -18.255136264.Subproblem 1
x + -18.5 = 18.255136264 Simplifying x + -18.5 = 18.255136264 Reorder the terms: -18.5 + x = 18.255136264 Solving -18.5 + x = 18.255136264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x = 18.255136264 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = 18.255136264 + 18.5 x = 18.255136264 + 18.5 Combine like terms: 18.255136264 + 18.5 = 36.755136264 x = 36.755136264 Simplifying x = 36.755136264Subproblem 2
x + -18.5 = -18.255136264 Simplifying x + -18.5 = -18.255136264 Reorder the terms: -18.5 + x = -18.255136264 Solving -18.5 + x = -18.255136264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x = -18.255136264 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = -18.255136264 + 18.5 x = -18.255136264 + 18.5 Combine like terms: -18.255136264 + 18.5 = 0.244863736 x = 0.244863736 Simplifying x = 0.244863736Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.755136264, 0.244863736}Solution
x = {36.755136264, 0.244863736}
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