2x^3+9x^2-10x=0

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Solution for 2x^3+9x^2-10x=0 equation:


Simplifying
2x3 + 9x2 + -10x = 0

Reorder the terms:
-10x + 9x2 + 2x3 = 0

Solving
-10x + 9x2 + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-10 + 9x + 2x2) = 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 '(-10 + 9x + 2x2)' equal to zero and attempt to solve: Simplifying -10 + 9x + 2x2 = 0 Solving -10 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5 + 4.5x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 4.5x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 4.5x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 4.5x + x2 = 0 + 5 4.5x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 4.5x + x2 = 5 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 5 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 5 + 5.0625 Combine like terms: 5 + 5.0625 = 10.0625 5.0625 + 4.5x + x2 = 10.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 10.0625 Calculate the square root of the right side: 3.172144385 Break this problem into two subproblems by setting (x + 2.25) equal to 3.172144385 and -3.172144385.

Subproblem 1

x + 2.25 = 3.172144385 Simplifying x + 2.25 = 3.172144385 Reorder the terms: 2.25 + x = 3.172144385 Solving 2.25 + x = 3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 3.172144385 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 3.172144385 + -2.25 x = 3.172144385 + -2.25 Combine like terms: 3.172144385 + -2.25 = 0.922144385 x = 0.922144385 Simplifying x = 0.922144385

Subproblem 2

x + 2.25 = -3.172144385 Simplifying x + 2.25 = -3.172144385 Reorder the terms: 2.25 + x = -3.172144385 Solving 2.25 + x = -3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -3.172144385 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -3.172144385 + -2.25 x = -3.172144385 + -2.25 Combine like terms: -3.172144385 + -2.25 = -5.422144385 x = -5.422144385 Simplifying x = -5.422144385

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.922144385, -5.422144385}

Solution

x = {0, 0.922144385, -5.422144385}

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