5x^4-44x^3+42x^2=0

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Solution for 5x^4-44x^3+42x^2=0 equation:


Simplifying
5x4 + -44x3 + 42x2 = 0

Reorder the terms:
42x2 + -44x3 + 5x4 = 0

Solving
42x2 + -44x3 + 5x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(42 + -44x + 5x2) = 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 '(42 + -44x + 5x2)' equal to zero and attempt to solve: Simplifying 42 + -44x + 5x2 = 0 Solving 42 + -44x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 8.4 + -8.8x + x2 = 0 Move the constant term to the right: Add '-8.4' to each side of the equation. 8.4 + -8.8x + -8.4 + x2 = 0 + -8.4 Reorder the terms: 8.4 + -8.4 + -8.8x + x2 = 0 + -8.4 Combine like terms: 8.4 + -8.4 = 0.0 0.0 + -8.8x + x2 = 0 + -8.4 -8.8x + x2 = 0 + -8.4 Combine like terms: 0 + -8.4 = -8.4 -8.8x + x2 = -8.4 The x term is -8.8x. Take half its coefficient (-4.4). Square it (19.36) and add it to both sides. Add '19.36' to each side of the equation. -8.8x + 19.36 + x2 = -8.4 + 19.36 Reorder the terms: 19.36 + -8.8x + x2 = -8.4 + 19.36 Combine like terms: -8.4 + 19.36 = 10.96 19.36 + -8.8x + x2 = 10.96 Factor a perfect square on the left side: (x + -4.4)(x + -4.4) = 10.96 Calculate the square root of the right side: 3.310589071 Break this problem into two subproblems by setting (x + -4.4) equal to 3.310589071 and -3.310589071.

Subproblem 1

x + -4.4 = 3.310589071 Simplifying x + -4.4 = 3.310589071 Reorder the terms: -4.4 + x = 3.310589071 Solving -4.4 + x = 3.310589071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.4' to each side of the equation. -4.4 + 4.4 + x = 3.310589071 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + x = 3.310589071 + 4.4 x = 3.310589071 + 4.4 Combine like terms: 3.310589071 + 4.4 = 7.710589071 x = 7.710589071 Simplifying x = 7.710589071

Subproblem 2

x + -4.4 = -3.310589071 Simplifying x + -4.4 = -3.310589071 Reorder the terms: -4.4 + x = -3.310589071 Solving -4.4 + x = -3.310589071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.4' to each side of the equation. -4.4 + 4.4 + x = -3.310589071 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + x = -3.310589071 + 4.4 x = -3.310589071 + 4.4 Combine like terms: -3.310589071 + 4.4 = 1.089410929 x = 1.089410929 Simplifying x = 1.089410929

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.710589071, 1.089410929}

Solution

x = {0, 7.710589071, 1.089410929}

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