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Simplifying 7x5 + 7x3 + -36x = 0 Reorder the terms: -36x + 7x3 + 7x5 = 0 Solving -36x + 7x3 + 7x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-36 + 7x2 + 7x4) = 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 '(-36 + 7x2 + 7x4)' equal to zero and attempt to solve: Simplifying -36 + 7x2 + 7x4 = 0 Solving -36 + 7x2 + 7x4 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -5.142857143 + x2 + x4 = 0 Move the constant term to the right: Add '5.142857143' to each side of the equation. -5.142857143 + x2 + 5.142857143 + x4 = 0 + 5.142857143 Reorder the terms: -5.142857143 + 5.142857143 + x2 + x4 = 0 + 5.142857143 Combine like terms: -5.142857143 + 5.142857143 = 0.000000000 0.000000000 + x2 + x4 = 0 + 5.142857143 x2 + x4 = 0 + 5.142857143 Combine like terms: 0 + 5.142857143 = 5.142857143 x2 + x4 = 5.142857143 The x term is x2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x4 = 5.142857143 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x4 = 5.142857143 + 0.25 Combine like terms: 5.142857143 + 0.25 = 5.392857143 1.25 + x4 = 5.392857143 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 5.392857143 Calculate the square root of the right side: 2.322252601 Break this problem into two subproblems by setting (x2 + 0.5) equal to 2.322252601 and -2.322252601.Subproblem 1
x2 + 0.5 = 2.322252601 Simplifying x2 + 0.5 = 2.322252601 Reorder the terms: 0.5 + x2 = 2.322252601 Solving 0.5 + x2 = 2.322252601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = 2.322252601 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 2.322252601 + -0.5 x2 = 2.322252601 + -0.5 Combine like terms: 2.322252601 + -0.5 = 1.822252601 x2 = 1.822252601 Simplifying x2 = 1.822252601 Take the square root of each side: x = {-1.349908368, 1.349908368}Subproblem 2
x2 + 0.5 = -2.322252601 Simplifying x2 + 0.5 = -2.322252601 Reorder the terms: 0.5 + x2 = -2.322252601 Solving 0.5 + x2 = -2.322252601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = -2.322252601 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -2.322252601 + -0.5 x2 = -2.322252601 + -0.5 Combine like terms: -2.322252601 + -0.5 = -2.822252601 x2 = -2.822252601 Simplifying x2 = -2.822252601 Reorder the terms: 2.822252601 + x2 = -2.822252601 + 2.822252601 Combine like terms: -2.822252601 + 2.822252601 = 0.000000000 2.822252601 + 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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