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Simplifying 0 = x5 + -4x4 + -4x3 Reorder the terms: 0 = -4x3 + -4x4 + x5 Solving 0 = -4x3 + -4x4 + x5 Solving for variable 'x'. Remove the zero: 4x3 + 4x4 + -1x5 = -4x3 + -4x4 + x5 + 4x3 + 4x4 + -1x5 Reorder the terms: 4x3 + 4x4 + -1x5 = -4x3 + 4x3 + -4x4 + 4x4 + x5 + -1x5 Combine like terms: -4x3 + 4x3 = 0 4x3 + 4x4 + -1x5 = 0 + -4x4 + 4x4 + x5 + -1x5 4x3 + 4x4 + -1x5 = -4x4 + 4x4 + x5 + -1x5 Combine like terms: -4x4 + 4x4 = 0 4x3 + 4x4 + -1x5 = 0 + x5 + -1x5 4x3 + 4x4 + -1x5 = x5 + -1x5 Combine like terms: x5 + -1x5 = 0 4x3 + 4x4 + -1x5 = 0 Factor out the Greatest Common Factor (GCF), 'x3'. x3(4 + 4x + -1x2) = 0Subproblem 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 '(4 + 4x + -1x2)' equal to zero and attempt to solve: Simplifying 4 + 4x + -1x2 = 0 Solving 4 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + -4x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -4x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -4x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -4x + x2 = 0 + 4 -4x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -4x + x2 = 4 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 4 + 4 Reorder the terms: 4 + -4x + x2 = 4 + 4 Combine like terms: 4 + 4 = 8 4 + -4x + x2 = 8 Factor a perfect square on the left side: (x + -2)(x + -2) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + -2) equal to 2.828427125 and -2.828427125.Subproblem 1
x + -2 = 2.828427125 Simplifying x + -2 = 2.828427125 Reorder the terms: -2 + x = 2.828427125 Solving -2 + x = 2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.828427125 + 2 x = 2.828427125 + 2 Combine like terms: 2.828427125 + 2 = 4.828427125 x = 4.828427125 Simplifying x = 4.828427125Subproblem 2
x + -2 = -2.828427125 Simplifying x + -2 = -2.828427125 Reorder the terms: -2 + x = -2.828427125 Solving -2 + x = -2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.828427125 + 2 x = -2.828427125 + 2 Combine like terms: -2.828427125 + 2 = -0.828427125 x = -0.828427125 Simplifying x = -0.828427125Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.828427125, -0.828427125}Solution
x = {4.828427125, -0.828427125}
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