25x^3-30x^5+35x=0

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Solution for 25x^3-30x^5+35x=0 equation:


Simplifying
25x3 + -30x5 + 35x = 0

Reorder the terms:
35x + 25x3 + -30x5 = 0

Solving
35x + 25x3 + -30x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(7 + 5x2 + -6x4) = 0

Ignore the factor 5.

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 = 0

Subproblem 2

Set the factor '(7 + 5x2 + -6x4)' equal to zero and attempt to solve: Simplifying 7 + 5x2 + -6x4 = 0 Solving 7 + 5x2 + -6x4 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -1.166666667 + -0.8333333333x2 + x4 = 0 Move the constant term to the right: Add '1.166666667' to each side of the equation. -1.166666667 + -0.8333333333x2 + 1.166666667 + x4 = 0 + 1.166666667 Reorder the terms: -1.166666667 + 1.166666667 + -0.8333333333x2 + x4 = 0 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + -0.8333333333x2 + x4 = 0 + 1.166666667 -0.8333333333x2 + x4 = 0 + 1.166666667 Combine like terms: 0 + 1.166666667 = 1.166666667 -0.8333333333x2 + x4 = 1.166666667 The x term is -0.8333333333x2. Take half its coefficient (-0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. -0.8333333333x2 + 0.1736111111 + x4 = 1.166666667 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333x2 + x4 = 1.166666667 + 0.1736111111 Combine like terms: 1.166666667 + 0.1736111111 = 1.3402777781 0.1736111111 + -0.8333333333x2 + x4 = 1.3402777781 Factor a perfect square on the left side: (x2 + -0.4166666667)(x2 + -0.4166666667) = 1.3402777781 Calculate the square root of the right side: 1.157703666 Break this problem into two subproblems by setting (x2 + -0.4166666667) equal to 1.157703666 and -1.157703666.

Subproblem 1

x2 + -0.4166666667 = 1.157703666 Simplifying x2 + -0.4166666667 = 1.157703666 Reorder the terms: -0.4166666667 + x2 = 1.157703666 Solving -0.4166666667 + x2 = 1.157703666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x2 = 1.157703666 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x2 = 1.157703666 + 0.4166666667 x2 = 1.157703666 + 0.4166666667 Combine like terms: 1.157703666 + 0.4166666667 = 1.5743703327 x2 = 1.5743703327 Simplifying x2 = 1.5743703327 Take the square root of each side: x = {-1.254739149, 1.254739149}

Subproblem 2

x2 + -0.4166666667 = -1.157703666 Simplifying x2 + -0.4166666667 = -1.157703666 Reorder the terms: -0.4166666667 + x2 = -1.157703666 Solving -0.4166666667 + x2 = -1.157703666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x2 = -1.157703666 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x2 = -1.157703666 + 0.4166666667 x2 = -1.157703666 + 0.4166666667 Combine like terms: -1.157703666 + 0.4166666667 = -0.7410369993 x2 = -0.7410369993 Simplifying x2 = -0.7410369993 Reorder the terms: 0.7410369993 + x2 = -0.7410369993 + 0.7410369993 Combine like terms: -0.7410369993 + 0.7410369993 = 0.0000000000 0.7410369993 + x2 = 0.0000000000 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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