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Simplifying x = 4x5 + -14x3 + -30x Reorder the terms: x = -30x + -14x3 + 4x5 Solving x = -30x + -14x3 + 4x5 Solving for variable 'x'. Combine like terms: x + 30x = 31x 31x + 14x3 + -4x5 = -30x + -14x3 + 4x5 + 30x + 14x3 + -4x5 Reorder the terms: 31x + 14x3 + -4x5 = -30x + 30x + -14x3 + 14x3 + 4x5 + -4x5 Combine like terms: -30x + 30x = 0 31x + 14x3 + -4x5 = 0 + -14x3 + 14x3 + 4x5 + -4x5 31x + 14x3 + -4x5 = -14x3 + 14x3 + 4x5 + -4x5 Combine like terms: -14x3 + 14x3 = 0 31x + 14x3 + -4x5 = 0 + 4x5 + -4x5 31x + 14x3 + -4x5 = 4x5 + -4x5 Combine like terms: 4x5 + -4x5 = 0 31x + 14x3 + -4x5 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(31 + 14x2 + -4x4) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(31 + 14x2 + -4x4)' equal to zero and attempt to solve: Simplifying 31 + 14x2 + -4x4 = 0 Solving 31 + 14x2 + -4x4 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -7.75 + -3.5x2 + x4 = 0 Move the constant term to the right: Add '7.75' to each side of the equation. -7.75 + -3.5x2 + 7.75 + x4 = 0 + 7.75 Reorder the terms: -7.75 + 7.75 + -3.5x2 + x4 = 0 + 7.75 Combine like terms: -7.75 + 7.75 = 0.00 0.00 + -3.5x2 + x4 = 0 + 7.75 -3.5x2 + x4 = 0 + 7.75 Combine like terms: 0 + 7.75 = 7.75 -3.5x2 + x4 = 7.75 The x term is -3.5x2. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x2 + 3.0625 + x4 = 7.75 + 3.0625 Reorder the terms: 3.0625 + -3.5x2 + x4 = 7.75 + 3.0625 Combine like terms: 7.75 + 3.0625 = 10.8125 3.0625 + -3.5x2 + x4 = 10.8125 Factor a perfect square on the left side: (x2 + -1.75)(x2 + -1.75) = 10.8125 Calculate the square root of the right side: 3.288236609 Break this problem into two subproblems by setting (x2 + -1.75) equal to 3.288236609 and -3.288236609.Subproblem 1
x2 + -1.75 = 3.288236609 Simplifying x2 + -1.75 = 3.288236609 Reorder the terms: -1.75 + x2 = 3.288236609 Solving -1.75 + x2 = 3.288236609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x2 = 3.288236609 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x2 = 3.288236609 + 1.75 x2 = 3.288236609 + 1.75 Combine like terms: 3.288236609 + 1.75 = 5.038236609 x2 = 5.038236609 Simplifying x2 = 5.038236609 Take the square root of each side: x = {-2.244601659, 2.244601659}Subproblem 2
x2 + -1.75 = -3.288236609 Simplifying x2 + -1.75 = -3.288236609 Reorder the terms: -1.75 + x2 = -3.288236609 Solving -1.75 + x2 = -3.288236609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x2 = -3.288236609 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x2 = -3.288236609 + 1.75 x2 = -3.288236609 + 1.75 Combine like terms: -3.288236609 + 1.75 = -1.538236609 x2 = -1.538236609 Simplifying x2 = -1.538236609 Reorder the terms: 1.538236609 + x2 = -1.538236609 + 1.538236609 Combine like terms: -1.538236609 + 1.538236609 = 0.000000000 1.538236609 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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