81x^2+36x-4=0

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Solution for 81x^2+36x-4=0 equation:


Simplifying
81x2 + 36x + -4 = 0

Reorder the terms:
-4 + 36x + 81x2 = 0

Solving
-4 + 36x + 81x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
81 the coefficient of the squared term: 

Divide each side by '81'.
-0.04938271605 + 0.4444444444x + x2 = 0

Move the constant term to the right:

Add '0.04938271605' to each side of the equation.
-0.04938271605 + 0.4444444444x + 0.04938271605 + x2 = 0 + 0.04938271605

Reorder the terms:
-0.04938271605 + 0.04938271605 + 0.4444444444x + x2 = 0 + 0.04938271605

Combine like terms: -0.04938271605 + 0.04938271605 = 0.00000000000
0.00000000000 + 0.4444444444x + x2 = 0 + 0.04938271605
0.4444444444x + x2 = 0 + 0.04938271605

Combine like terms: 0 + 0.04938271605 = 0.04938271605
0.4444444444x + x2 = 0.04938271605

The x term is 0.4444444444x.  Take half its coefficient (0.2222222222).
Square it (0.04938271604) and add it to both sides.

Add '0.04938271604' to each side of the equation.
0.4444444444x + 0.04938271604 + x2 = 0.04938271605 + 0.04938271604

Reorder the terms:
0.04938271604 + 0.4444444444x + x2 = 0.04938271605 + 0.04938271604

Combine like terms: 0.04938271605 + 0.04938271604 = 0.09876543209
0.04938271604 + 0.4444444444x + x2 = 0.09876543209

Factor a perfect square on the left side:
(x + 0.2222222222)(x + 0.2222222222) = 0.09876543209

Calculate the square root of the right side: 0.314269681

Break this problem into two subproblems by setting 
(x + 0.2222222222) equal to 0.314269681 and -0.314269681.

Subproblem 1

x + 0.2222222222 = 0.314269681 Simplifying x + 0.2222222222 = 0.314269681 Reorder the terms: 0.2222222222 + x = 0.314269681 Solving 0.2222222222 + x = 0.314269681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = 0.314269681 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = 0.314269681 + -0.2222222222 x = 0.314269681 + -0.2222222222 Combine like terms: 0.314269681 + -0.2222222222 = 0.0920474588 x = 0.0920474588 Simplifying x = 0.0920474588

Subproblem 2

x + 0.2222222222 = -0.314269681 Simplifying x + 0.2222222222 = -0.314269681 Reorder the terms: 0.2222222222 + x = -0.314269681 Solving 0.2222222222 + x = -0.314269681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = -0.314269681 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = -0.314269681 + -0.2222222222 x = -0.314269681 + -0.2222222222 Combine like terms: -0.314269681 + -0.2222222222 = -0.5364919032 x = -0.5364919032 Simplifying x = -0.5364919032

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.0920474588, -0.5364919032}

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