81x^2+18x-6=0

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Solution for 81x^2+18x-6=0 equation:


Simplifying
81x2 + 18x + -6 = 0

Reorder the terms:
-6 + 18x + 81x2 = 0

Solving
-6 + 18x + 81x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 6x + 27x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-2 + 6x + 27x2)' equal to zero and attempt to solve: Simplifying -2 + 6x + 27x2 = 0 Solving -2 + 6x + 27x2 = 0 Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. -0.07407407407 + 0.2222222222x + x2 = 0 Move the constant term to the right: Add '0.07407407407' to each side of the equation. -0.07407407407 + 0.2222222222x + 0.07407407407 + x2 = 0 + 0.07407407407 Reorder the terms: -0.07407407407 + 0.07407407407 + 0.2222222222x + x2 = 0 + 0.07407407407 Combine like terms: -0.07407407407 + 0.07407407407 = 0.00000000000 0.00000000000 + 0.2222222222x + x2 = 0 + 0.07407407407 0.2222222222x + x2 = 0 + 0.07407407407 Combine like terms: 0 + 0.07407407407 = 0.07407407407 0.2222222222x + x2 = 0.07407407407 The x term is 0.2222222222x. Take half its coefficient (0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. 0.2222222222x + 0.01234567901 + x2 = 0.07407407407 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222x + x2 = 0.07407407407 + 0.01234567901 Combine like terms: 0.07407407407 + 0.01234567901 = 0.08641975308 0.01234567901 + 0.2222222222x + x2 = 0.08641975308 Factor a perfect square on the left side: (x + 0.1111111111)(x + 0.1111111111) = 0.08641975308 Calculate the square root of the right side: 0.293972368 Break this problem into two subproblems by setting (x + 0.1111111111) equal to 0.293972368 and -0.293972368.

Subproblem 1

x + 0.1111111111 = 0.293972368 Simplifying x + 0.1111111111 = 0.293972368 Reorder the terms: 0.1111111111 + x = 0.293972368 Solving 0.1111111111 + x = 0.293972368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + x = 0.293972368 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = 0.293972368 + -0.1111111111 x = 0.293972368 + -0.1111111111 Combine like terms: 0.293972368 + -0.1111111111 = 0.1828612569 x = 0.1828612569 Simplifying x = 0.1828612569

Subproblem 2

x + 0.1111111111 = -0.293972368 Simplifying x + 0.1111111111 = -0.293972368 Reorder the terms: 0.1111111111 + x = -0.293972368 Solving 0.1111111111 + x = -0.293972368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + x = -0.293972368 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = -0.293972368 + -0.1111111111 x = -0.293972368 + -0.1111111111 Combine like terms: -0.293972368 + -0.1111111111 = -0.4050834791 x = -0.4050834791 Simplifying x = -0.4050834791

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.1828612569, -0.4050834791}

Solution

x = {0.1828612569, -0.4050834791}

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