2*(6x-9-27x)*x+3=0

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Solution for 2*(6x-9-27x)*x+3=0 equation:


Simplifying
2(6x + -9 + -27x) * x + 3 = 0

Reorder the terms:
2(-9 + 6x + -27x) * x + 3 = 0

Combine like terms: 6x + -27x = -21x
2(-9 + -21x) * x + 3 = 0

Reorder the terms for easier multiplication:
2x(-9 + -21x) + 3 = 0
(-9 * 2x + -21x * 2x) + 3 = 0
(-18x + -42x2) + 3 = 0

Reorder the terms:
3 + -18x + -42x2 = 0

Solving
3 + -18x + -42x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -6x + -14x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(1 + -6x + -14x2)' equal to zero and attempt to solve: Simplifying 1 + -6x + -14x2 = 0 Solving 1 + -6x + -14x2 = 0 Begin completing the square. Divide all terms by -14 the coefficient of the squared term: Divide each side by '-14'. -0.07142857143 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '0.07142857143' to each side of the equation. -0.07142857143 + 0.4285714286x + 0.07142857143 + x2 = 0 + 0.07142857143 Reorder the terms: -0.07142857143 + 0.07142857143 + 0.4285714286x + x2 = 0 + 0.07142857143 Combine like terms: -0.07142857143 + 0.07142857143 = 0.00000000000 0.00000000000 + 0.4285714286x + x2 = 0 + 0.07142857143 0.4285714286x + x2 = 0 + 0.07142857143 Combine like terms: 0 + 0.07142857143 = 0.07142857143 0.4285714286x + x2 = 0.07142857143 The x term is 0.4285714286x. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286x + 0.04591836735 + x2 = 0.07142857143 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = 0.07142857143 + 0.04591836735 Combine like terms: 0.07142857143 + 0.04591836735 = 0.11734693878 0.04591836735 + 0.4285714286x + x2 = 0.11734693878 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = 0.11734693878 Calculate the square root of the right side: 0.342559395 Break this problem into two subproblems by setting (x + 0.2142857143) equal to 0.342559395 and -0.342559395.

Subproblem 1

x + 0.2142857143 = 0.342559395 Simplifying x + 0.2142857143 = 0.342559395 Reorder the terms: 0.2142857143 + x = 0.342559395 Solving 0.2142857143 + x = 0.342559395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = 0.342559395 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = 0.342559395 + -0.2142857143 x = 0.342559395 + -0.2142857143 Combine like terms: 0.342559395 + -0.2142857143 = 0.1282736807 x = 0.1282736807 Simplifying x = 0.1282736807

Subproblem 2

x + 0.2142857143 = -0.342559395 Simplifying x + 0.2142857143 = -0.342559395 Reorder the terms: 0.2142857143 + x = -0.342559395 Solving 0.2142857143 + x = -0.342559395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = -0.342559395 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = -0.342559395 + -0.2142857143 x = -0.342559395 + -0.2142857143 Combine like terms: -0.342559395 + -0.2142857143 = -0.5568451093 x = -0.5568451093 Simplifying x = -0.5568451093

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.1282736807, -0.5568451093}

Solution

x = {0.1282736807, -0.5568451093}

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