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Simplifying (9x + 5)(9x + 5) = 126 Reorder the terms: (5 + 9x)(9x + 5) = 126 Reorder the terms: (5 + 9x)(5 + 9x) = 126 Multiply (5 + 9x) * (5 + 9x) (5(5 + 9x) + 9x * (5 + 9x)) = 126 ((5 * 5 + 9x * 5) + 9x * (5 + 9x)) = 126 ((25 + 45x) + 9x * (5 + 9x)) = 126 (25 + 45x + (5 * 9x + 9x * 9x)) = 126 (25 + 45x + (45x + 81x2)) = 126 Combine like terms: 45x + 45x = 90x (25 + 90x + 81x2) = 126 Solving 25 + 90x + 81x2 = 126 Solving for variable 'x'. Reorder the terms: 25 + -126 + 90x + 81x2 = 126 + -126 Combine like terms: 25 + -126 = -101 -101 + 90x + 81x2 = 126 + -126 Combine like terms: 126 + -126 = 0 -101 + 90x + 81x2 = 0 Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. -1.24691358 + 1.111111111x + x2 = 0 Move the constant term to the right: Add '1.24691358' to each side of the equation. -1.24691358 + 1.111111111x + 1.24691358 + x2 = 0 + 1.24691358 Reorder the terms: -1.24691358 + 1.24691358 + 1.111111111x + x2 = 0 + 1.24691358 Combine like terms: -1.24691358 + 1.24691358 = 0.00000000 0.00000000 + 1.111111111x + x2 = 0 + 1.24691358 1.111111111x + x2 = 0 + 1.24691358 Combine like terms: 0 + 1.24691358 = 1.24691358 1.111111111x + x2 = 1.24691358 The x term is 1.111111111x. Take half its coefficient (0.5555555555). Square it (0.3086419752) and add it to both sides. Add '0.3086419752' to each side of the equation. 1.111111111x + 0.3086419752 + x2 = 1.24691358 + 0.3086419752 Reorder the terms: 0.3086419752 + 1.111111111x + x2 = 1.24691358 + 0.3086419752 Combine like terms: 1.24691358 + 0.3086419752 = 1.5555555552 0.3086419752 + 1.111111111x + x2 = 1.5555555552 Factor a perfect square on the left side: (x + 0.5555555555)(x + 0.5555555555) = 1.5555555552 Calculate the square root of the right side: 1.247219129 Break this problem into two subproblems by setting (x + 0.5555555555) equal to 1.247219129 and -1.247219129.Subproblem 1
x + 0.5555555555 = 1.247219129 Simplifying x + 0.5555555555 = 1.247219129 Reorder the terms: 0.5555555555 + x = 1.247219129 Solving 0.5555555555 + x = 1.247219129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + x = 1.247219129 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + x = 1.247219129 + -0.5555555555 x = 1.247219129 + -0.5555555555 Combine like terms: 1.247219129 + -0.5555555555 = 0.6916635735 x = 0.6916635735 Simplifying x = 0.6916635735Subproblem 2
x + 0.5555555555 = -1.247219129 Simplifying x + 0.5555555555 = -1.247219129 Reorder the terms: 0.5555555555 + x = -1.247219129 Solving 0.5555555555 + x = -1.247219129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + x = -1.247219129 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + x = -1.247219129 + -0.5555555555 x = -1.247219129 + -0.5555555555 Combine like terms: -1.247219129 + -0.5555555555 = -1.8027746845 x = -1.8027746845 Simplifying x = -1.8027746845Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6916635735, -1.8027746845}
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