(9x)(9x)+21x-8=0

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Solution for (9x)(9x)+21x-8=0 equation:


Simplifying
(9x)(9x) + 21x + -8 = 0

Remove parenthesis around (9x)
9x(9x) + 21x + -8 = 0

Remove parenthesis around (9x)
9x * 9x + 21x + -8 = 0

Reorder the terms for easier multiplication:
9 * 9x * x + 21x + -8 = 0

Multiply 9 * 9
81x * x + 21x + -8 = 0

Multiply x * x
81x2 + 21x + -8 = 0

Reorder the terms:
-8 + 21x + 81x2 = 0

Solving
-8 + 21x + 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'.
-0.0987654321 + 0.2592592593x + x2 = 0

Move the constant term to the right:

Add '0.0987654321' to each side of the equation.
-0.0987654321 + 0.2592592593x + 0.0987654321 + x2 = 0 + 0.0987654321

Reorder the terms:
-0.0987654321 + 0.0987654321 + 0.2592592593x + x2 = 0 + 0.0987654321

Combine like terms: -0.0987654321 + 0.0987654321 = 0.0000000000
0.0000000000 + 0.2592592593x + x2 = 0 + 0.0987654321
0.2592592593x + x2 = 0 + 0.0987654321

Combine like terms: 0 + 0.0987654321 = 0.0987654321
0.2592592593x + x2 = 0.0987654321

The x term is 0.2592592593x.  Take half its coefficient (0.1296296297).
Square it (0.01680384090) and add it to both sides.

Add '0.01680384090' to each side of the equation.
0.2592592593x + 0.01680384090 + x2 = 0.0987654321 + 0.01680384090

Reorder the terms:
0.01680384090 + 0.2592592593x + x2 = 0.0987654321 + 0.01680384090

Combine like terms: 0.0987654321 + 0.01680384090 = 0.115569273
0.01680384090 + 0.2592592593x + x2 = 0.115569273

Factor a perfect square on the left side:
(x + 0.1296296297)(x + 0.1296296297) = 0.115569273

Calculate the square root of the right side: 0.33995481

Break this problem into two subproblems by setting 
(x + 0.1296296297) equal to 0.33995481 and -0.33995481.

Subproblem 1

x + 0.1296296297 = 0.33995481 Simplifying x + 0.1296296297 = 0.33995481 Reorder the terms: 0.1296296297 + x = 0.33995481 Solving 0.1296296297 + x = 0.33995481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1296296297' to each side of the equation. 0.1296296297 + -0.1296296297 + x = 0.33995481 + -0.1296296297 Combine like terms: 0.1296296297 + -0.1296296297 = 0.0000000000 0.0000000000 + x = 0.33995481 + -0.1296296297 x = 0.33995481 + -0.1296296297 Combine like terms: 0.33995481 + -0.1296296297 = 0.2103251803 x = 0.2103251803 Simplifying x = 0.2103251803

Subproblem 2

x + 0.1296296297 = -0.33995481 Simplifying x + 0.1296296297 = -0.33995481 Reorder the terms: 0.1296296297 + x = -0.33995481 Solving 0.1296296297 + x = -0.33995481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1296296297' to each side of the equation. 0.1296296297 + -0.1296296297 + x = -0.33995481 + -0.1296296297 Combine like terms: 0.1296296297 + -0.1296296297 = 0.0000000000 0.0000000000 + x = -0.33995481 + -0.1296296297 x = -0.33995481 + -0.1296296297 Combine like terms: -0.33995481 + -0.1296296297 = -0.4695844397 x = -0.4695844397 Simplifying x = -0.4695844397

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.2103251803, -0.4695844397}

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