2x*3+3x*2x=3

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Solution for 2x*3+3x*2x=3 equation:


Simplifying
2x * 3 + 3x * 2x = 3

Reorder the terms for easier multiplication:
2 * 3x + 3x * 2x = 3

Multiply 2 * 3
6x + 3x * 2x = 3

Reorder the terms for easier multiplication:
6x + 3 * 2x * x = 3

Multiply 3 * 2
6x + 6x * x = 3

Multiply x * x
6x + 6x2 = 3

Solving
6x + 6x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + 6x + 6x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 6x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 2x + 2x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-1 + 2x + 2x2)' equal to zero and attempt to solve: Simplifying -1 + 2x + 2x2 = 0 Solving -1 + 2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x + x2 = 0 + 0.5 x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 x + x2 = 0.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 0.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.5 + 0.25 Combine like terms: 0.5 + 0.25 = 0.75 1.25 + x2 = 0.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.75 Calculate the square root of the right side: 0.866025404 Break this problem into two subproblems by setting (x + 0.5) equal to 0.866025404 and -0.866025404.

Subproblem 1

x + 0.5 = 0.866025404 Simplifying x + 0.5 = 0.866025404 Reorder the terms: 0.5 + x = 0.866025404 Solving 0.5 + x = 0.866025404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.866025404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.866025404 + -0.5 x = 0.866025404 + -0.5 Combine like terms: 0.866025404 + -0.5 = 0.366025404 x = 0.366025404 Simplifying x = 0.366025404

Subproblem 2

x + 0.5 = -0.866025404 Simplifying x + 0.5 = -0.866025404 Reorder the terms: 0.5 + x = -0.866025404 Solving 0.5 + x = -0.866025404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.866025404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.866025404 + -0.5 x = -0.866025404 + -0.5 Combine like terms: -0.866025404 + -0.5 = -1.366025404 x = -1.366025404 Simplifying x = -1.366025404

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.366025404, -1.366025404}

Solution

x = {0.366025404, -1.366025404}

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