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Simplifying 0 = 12x2 + 9x + 1 Reorder the terms: 0 = 1 + 9x + 12x2 Solving 0 = 1 + 9x + 12x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + -9x + -12x2 = 1 + 9x + 12x2 + -1 + -9x + -12x2 Reorder the terms: -1 + -9x + -12x2 = 1 + -1 + 9x + -9x + 12x2 + -12x2 Combine like terms: 1 + -1 = 0 -1 + -9x + -12x2 = 0 + 9x + -9x + 12x2 + -12x2 -1 + -9x + -12x2 = 9x + -9x + 12x2 + -12x2 Combine like terms: 9x + -9x = 0 -1 + -9x + -12x2 = 0 + 12x2 + -12x2 -1 + -9x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -1 + -9x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 9x + 12x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 9x + 12x2)' equal to zero and attempt to solve: Simplifying 1 + 9x + 12x2 = 0 Solving 1 + 9x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.08333333333 + 0.75x + x2 = 0 Move the constant term to the right: Add '-0.08333333333' to each side of the equation. 0.08333333333 + 0.75x + -0.08333333333 + x2 = 0 + -0.08333333333 Reorder the terms: 0.08333333333 + -0.08333333333 + 0.75x + x2 = 0 + -0.08333333333 Combine like terms: 0.08333333333 + -0.08333333333 = 0.00000000000 0.00000000000 + 0.75x + x2 = 0 + -0.08333333333 0.75x + x2 = 0 + -0.08333333333 Combine like terms: 0 + -0.08333333333 = -0.08333333333 0.75x + x2 = -0.08333333333 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = -0.08333333333 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = -0.08333333333 + 0.140625 Combine like terms: -0.08333333333 + 0.140625 = 0.05729166667 0.140625 + 0.75x + x2 = 0.05729166667 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 0.05729166667 Calculate the square root of the right side: 0.239356777 Break this problem into two subproblems by setting (x + 0.375) equal to 0.239356777 and -0.239356777.Subproblem 1
x + 0.375 = 0.239356777 Simplifying x + 0.375 = 0.239356777 Reorder the terms: 0.375 + x = 0.239356777 Solving 0.375 + x = 0.239356777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 0.239356777 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 0.239356777 + -0.375 x = 0.239356777 + -0.375 Combine like terms: 0.239356777 + -0.375 = -0.135643223 x = -0.135643223 Simplifying x = -0.135643223Subproblem 2
x + 0.375 = -0.239356777 Simplifying x + 0.375 = -0.239356777 Reorder the terms: 0.375 + x = -0.239356777 Solving 0.375 + x = -0.239356777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -0.239356777 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -0.239356777 + -0.375 x = -0.239356777 + -0.375 Combine like terms: -0.239356777 + -0.375 = -0.614356777 x = -0.614356777 Simplifying x = -0.614356777Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.135643223, -0.614356777}Solution
x = {-0.135643223, -0.614356777}
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