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Simplifying 32x5 + -160x3 + 120x = 0 Reorder the terms: 120x + -160x3 + 32x5 = 0 Solving 120x + -160x3 + 32x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8x'. 8x(15 + -20x2 + 4x4) = 0 Ignore the factor 8.Subproblem 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 '(15 + -20x2 + 4x4)' equal to zero and attempt to solve: Simplifying 15 + -20x2 + 4x4 = 0 Solving 15 + -20x2 + 4x4 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.75 + -5x2 + x4 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -5x2 + -3.75 + x4 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + -5x2 + x4 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -5x2 + x4 = 0 + -3.75 -5x2 + x4 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 -5x2 + x4 = -3.75 The x term is -5x2. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x2 + 6.25 + x4 = -3.75 + 6.25 Reorder the terms: 6.25 + -5x2 + x4 = -3.75 + 6.25 Combine like terms: -3.75 + 6.25 = 2.5 6.25 + -5x2 + x4 = 2.5 Factor a perfect square on the left side: (x2 + -2.5)(x2 + -2.5) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (x2 + -2.5) equal to 1.58113883 and -1.58113883.Subproblem 1
x2 + -2.5 = 1.58113883 Simplifying x2 + -2.5 = 1.58113883 Reorder the terms: -2.5 + x2 = 1.58113883 Solving -2.5 + x2 = 1.58113883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x2 = 1.58113883 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x2 = 1.58113883 + 2.5 x2 = 1.58113883 + 2.5 Combine like terms: 1.58113883 + 2.5 = 4.08113883 x2 = 4.08113883 Simplifying x2 = 4.08113883 Take the square root of each side: x = {-2.02018287, 2.02018287}Subproblem 2
x2 + -2.5 = -1.58113883 Simplifying x2 + -2.5 = -1.58113883 Reorder the terms: -2.5 + x2 = -1.58113883 Solving -2.5 + x2 = -1.58113883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x2 = -1.58113883 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x2 = -1.58113883 + 2.5 x2 = -1.58113883 + 2.5 Combine like terms: -1.58113883 + 2.5 = 0.91886117 x2 = 0.91886117 Simplifying x2 = 0.91886117 Take the square root of each side: x = {-0.958572465, 0.958572465}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.02018287, 2.02018287, -0.958572465, 0.958572465}Solution
x = {0, -2.02018287, 2.02018287, -0.958572465, 0.958572465}
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