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