92x^3+51x^2+26x^4=

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Solution for 92x^3+51x^2+26x^4= equation:


Simplifying
92x3 + 51x2 + 26x4 = 0

Reorder the terms:
51x2 + 92x3 + 26x4 = 0

Solving
51x2 + 92x3 + 26x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(51 + 92x + 26x2) = 0

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 '(51 + 92x + 26x2)' equal to zero and attempt to solve: Simplifying 51 + 92x + 26x2 = 0 Solving 51 + 92x + 26x2 = 0 Begin completing the square. Divide all terms by 26 the coefficient of the squared term: Divide each side by '26'. 1.961538462 + 3.538461538x + x2 = 0 Move the constant term to the right: Add '-1.961538462' to each side of the equation. 1.961538462 + 3.538461538x + -1.961538462 + x2 = 0 + -1.961538462 Reorder the terms: 1.961538462 + -1.961538462 + 3.538461538x + x2 = 0 + -1.961538462 Combine like terms: 1.961538462 + -1.961538462 = 0.000000000 0.000000000 + 3.538461538x + x2 = 0 + -1.961538462 3.538461538x + x2 = 0 + -1.961538462 Combine like terms: 0 + -1.961538462 = -1.961538462 3.538461538x + x2 = -1.961538462 The x term is 3.538461538x. Take half its coefficient (1.769230769). Square it (3.130177514) and add it to both sides. Add '3.130177514' to each side of the equation. 3.538461538x + 3.130177514 + x2 = -1.961538462 + 3.130177514 Reorder the terms: 3.130177514 + 3.538461538x + x2 = -1.961538462 + 3.130177514 Combine like terms: -1.961538462 + 3.130177514 = 1.168639052 3.130177514 + 3.538461538x + x2 = 1.168639052 Factor a perfect square on the left side: (x + 1.769230769)(x + 1.769230769) = 1.168639052 Calculate the square root of the right side: 1.081036101 Break this problem into two subproblems by setting (x + 1.769230769) equal to 1.081036101 and -1.081036101.

Subproblem 1

x + 1.769230769 = 1.081036101 Simplifying x + 1.769230769 = 1.081036101 Reorder the terms: 1.769230769 + x = 1.081036101 Solving 1.769230769 + x = 1.081036101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.769230769' to each side of the equation. 1.769230769 + -1.769230769 + x = 1.081036101 + -1.769230769 Combine like terms: 1.769230769 + -1.769230769 = 0.000000000 0.000000000 + x = 1.081036101 + -1.769230769 x = 1.081036101 + -1.769230769 Combine like terms: 1.081036101 + -1.769230769 = -0.688194668 x = -0.688194668 Simplifying x = -0.688194668

Subproblem 2

x + 1.769230769 = -1.081036101 Simplifying x + 1.769230769 = -1.081036101 Reorder the terms: 1.769230769 + x = -1.081036101 Solving 1.769230769 + x = -1.081036101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.769230769' to each side of the equation. 1.769230769 + -1.769230769 + x = -1.081036101 + -1.769230769 Combine like terms: 1.769230769 + -1.769230769 = 0.000000000 0.000000000 + x = -1.081036101 + -1.769230769 x = -1.081036101 + -1.769230769 Combine like terms: -1.081036101 + -1.769230769 = -2.85026687 x = -2.85026687 Simplifying x = -2.85026687

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.688194668, -2.85026687}

Solution

x = {0, -0.688194668, -2.85026687}

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