2x^2-6x^4=56x^3

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Solution for 2x^2-6x^4=56x^3 equation:


Simplifying
2x2 + -6x4 = 56x3

Solving
2x2 + -6x4 = 56x3

Solving for variable 'x'.

Reorder the terms:
2x2 + -56x3 + -6x4 = 56x3 + -56x3

Combine like terms: 56x3 + -56x3 = 0
2x2 + -56x3 + -6x4 = 0

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(1 + -28x + -3x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}

Subproblem 2

Set the factor '(1 + -28x + -3x2)' equal to zero and attempt to solve: Simplifying 1 + -28x + -3x2 = 0 Solving 1 + -28x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -0.3333333333 + 9.333333333x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 9.333333333x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 9.333333333x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 9.333333333x + x2 = 0 + 0.3333333333 9.333333333x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 9.333333333x + x2 = 0.3333333333 The x term is 9.333333333x. Take half its coefficient (4.666666667). Square it (21.77777778) and add it to both sides. Add '21.77777778' to each side of the equation. 9.333333333x + 21.77777778 + x2 = 0.3333333333 + 21.77777778 Reorder the terms: 21.77777778 + 9.333333333x + x2 = 0.3333333333 + 21.77777778 Combine like terms: 0.3333333333 + 21.77777778 = 22.1111111133 21.77777778 + 9.333333333x + x2 = 22.1111111133 Factor a perfect square on the left side: (x + 4.666666667)(x + 4.666666667) = 22.1111111133 Calculate the square root of the right side: 4.702245327 Break this problem into two subproblems by setting (x + 4.666666667) equal to 4.702245327 and -4.702245327.

Subproblem 1

x + 4.666666667 = 4.702245327 Simplifying x + 4.666666667 = 4.702245327 Reorder the terms: 4.666666667 + x = 4.702245327 Solving 4.666666667 + x = 4.702245327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.666666667' to each side of the equation. 4.666666667 + -4.666666667 + x = 4.702245327 + -4.666666667 Combine like terms: 4.666666667 + -4.666666667 = 0.000000000 0.000000000 + x = 4.702245327 + -4.666666667 x = 4.702245327 + -4.666666667 Combine like terms: 4.702245327 + -4.666666667 = 0.03557866 x = 0.03557866 Simplifying x = 0.03557866

Subproblem 2

x + 4.666666667 = -4.702245327 Simplifying x + 4.666666667 = -4.702245327 Reorder the terms: 4.666666667 + x = -4.702245327 Solving 4.666666667 + x = -4.702245327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.666666667' to each side of the equation. 4.666666667 + -4.666666667 + x = -4.702245327 + -4.666666667 Combine like terms: 4.666666667 + -4.666666667 = 0.000000000 0.000000000 + x = -4.702245327 + -4.666666667 x = -4.702245327 + -4.666666667 Combine like terms: -4.702245327 + -4.666666667 = -9.368911994 x = -9.368911994 Simplifying x = -9.368911994

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.03557866, -9.368911994}

Solution

x = {0, 0.03557866, -9.368911994}

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