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Simplifying 3x5 + -18x3 + 25x = 0 Reorder the terms: 25x + -18x3 + 3x5 = 0 Solving 25x + -18x3 + 3x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(25 + -18x2 + 3x4) = 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 '(25 + -18x2 + 3x4)' equal to zero and attempt to solve: Simplifying 25 + -18x2 + 3x4 = 0 Solving 25 + -18x2 + 3x4 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 8.333333333 + -6x2 + x4 = 0 Move the constant term to the right: Add '-8.333333333' to each side of the equation. 8.333333333 + -6x2 + -8.333333333 + x4 = 0 + -8.333333333 Reorder the terms: 8.333333333 + -8.333333333 + -6x2 + x4 = 0 + -8.333333333 Combine like terms: 8.333333333 + -8.333333333 = 0.000000000 0.000000000 + -6x2 + x4 = 0 + -8.333333333 -6x2 + x4 = 0 + -8.333333333 Combine like terms: 0 + -8.333333333 = -8.333333333 -6x2 + x4 = -8.333333333 The x term is -6x2. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x2 + 9 + x4 = -8.333333333 + 9 Reorder the terms: 9 + -6x2 + x4 = -8.333333333 + 9 Combine like terms: -8.333333333 + 9 = 0.666666667 9 + -6x2 + x4 = 0.666666667 Factor a perfect square on the left side: (x2 + -3)(x2 + -3) = 0.666666667 Calculate the square root of the right side: 0.816496581 Break this problem into two subproblems by setting (x2 + -3) equal to 0.816496581 and -0.816496581.Subproblem 1
x2 + -3 = 0.816496581 Simplifying x2 + -3 = 0.816496581 Reorder the terms: -3 + x2 = 0.816496581 Solving -3 + x2 = 0.816496581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x2 = 0.816496581 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = 0.816496581 + 3 x2 = 0.816496581 + 3 Combine like terms: 0.816496581 + 3 = 3.816496581 x2 = 3.816496581 Simplifying x2 = 3.816496581 Take the square root of each side: x = {-1.95358557, 1.95358557}Subproblem 2
x2 + -3 = -0.816496581 Simplifying x2 + -3 = -0.816496581 Reorder the terms: -3 + x2 = -0.816496581 Solving -3 + x2 = -0.816496581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x2 = -0.816496581 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = -0.816496581 + 3 x2 = -0.816496581 + 3 Combine like terms: -0.816496581 + 3 = 2.183503419 x2 = 2.183503419 Simplifying x2 = 2.183503419 Take the square root of each side: x = {-1.477668237, 1.477668237}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.95358557, 1.95358557, -1.477668237, 1.477668237}Solution
x = {0, -1.95358557, 1.95358557, -1.477668237, 1.477668237}
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