5x^3+8x^2=18x

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Solution for 5x^3+8x^2=18x equation:


Simplifying
5x3 + 8x2 = 18x

Reorder the terms:
8x2 + 5x3 = 18x

Solving
8x2 + 5x3 = 18x

Solving for variable 'x'.

Reorder the terms:
-18x + 8x2 + 5x3 = 18x + -18x

Combine like terms: 18x + -18x = 0
-18x + 8x2 + 5x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-18 + 8x + 5x2) = 0

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 '(-18 + 8x + 5x2)' equal to zero and attempt to solve: Simplifying -18 + 8x + 5x2 = 0 Solving -18 + 8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.6 + 1.6x + x2 = 0 Move the constant term to the right: Add '3.6' to each side of the equation. -3.6 + 1.6x + 3.6 + x2 = 0 + 3.6 Reorder the terms: -3.6 + 3.6 + 1.6x + x2 = 0 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + 1.6x + x2 = 0 + 3.6 1.6x + x2 = 0 + 3.6 Combine like terms: 0 + 3.6 = 3.6 1.6x + x2 = 3.6 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = 3.6 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 3.6 + 0.64 Combine like terms: 3.6 + 0.64 = 4.24 0.64 + 1.6x + x2 = 4.24 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 4.24 Calculate the square root of the right side: 2.059126028 Break this problem into two subproblems by setting (x + 0.8) equal to 2.059126028 and -2.059126028.

Subproblem 1

x + 0.8 = 2.059126028 Simplifying x + 0.8 = 2.059126028 Reorder the terms: 0.8 + x = 2.059126028 Solving 0.8 + x = 2.059126028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 2.059126028 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 2.059126028 + -0.8 x = 2.059126028 + -0.8 Combine like terms: 2.059126028 + -0.8 = 1.259126028 x = 1.259126028 Simplifying x = 1.259126028

Subproblem 2

x + 0.8 = -2.059126028 Simplifying x + 0.8 = -2.059126028 Reorder the terms: 0.8 + x = -2.059126028 Solving 0.8 + x = -2.059126028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -2.059126028 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -2.059126028 + -0.8 x = -2.059126028 + -0.8 Combine like terms: -2.059126028 + -0.8 = -2.859126028 x = -2.859126028 Simplifying x = -2.859126028

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.259126028, -2.859126028}

Solution

x = {0, 1.259126028, -2.859126028}

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