10x^3+40x^2=16x

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Solution for 10x^3+40x^2=16x equation:


Simplifying
10x3 + 40x2 = 16x

Reorder the terms:
40x2 + 10x3 = 16x

Solving
40x2 + 10x3 = 16x

Solving for variable 'x'.

Reorder the terms:
-16x + 40x2 + 10x3 = 16x + -16x

Combine like terms: 16x + -16x = 0
-16x + 40x2 + 10x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-8 + 20x + 5x2) = 0

Ignore the factor 2.

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 '(-8 + 20x + 5x2)' equal to zero and attempt to solve: Simplifying -8 + 20x + 5x2 = 0 Solving -8 + 20x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.6 + 4x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + 4x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + 4x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + 4x + x2 = 0 + 1.6 4x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 4x + x2 = 1.6 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 1.6 + 4 Reorder the terms: 4 + 4x + x2 = 1.6 + 4 Combine like terms: 1.6 + 4 = 5.6 4 + 4x + x2 = 5.6 Factor a perfect square on the left side: (x + 2)(x + 2) = 5.6 Calculate the square root of the right side: 2.366431913 Break this problem into two subproblems by setting (x + 2) equal to 2.366431913 and -2.366431913.

Subproblem 1

x + 2 = 2.366431913 Simplifying x + 2 = 2.366431913 Reorder the terms: 2 + x = 2.366431913 Solving 2 + x = 2.366431913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.366431913 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.366431913 + -2 x = 2.366431913 + -2 Combine like terms: 2.366431913 + -2 = 0.366431913 x = 0.366431913 Simplifying x = 0.366431913

Subproblem 2

x + 2 = -2.366431913 Simplifying x + 2 = -2.366431913 Reorder the terms: 2 + x = -2.366431913 Solving 2 + x = -2.366431913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.366431913 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.366431913 + -2 x = -2.366431913 + -2 Combine like terms: -2.366431913 + -2 = -4.366431913 x = -4.366431913 Simplifying x = -4.366431913

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.366431913, -4.366431913}

Solution

x = {0, 0.366431913, -4.366431913}

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