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Simplifying 9x2 + 4x + -108 = 0 Reorder the terms: -108 + 4x + 9x2 = 0 Solving -108 + 4x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -12 + 0.4444444444x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 0.4444444444x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 0.4444444444x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 0.4444444444x + x2 = 0 + 12 0.4444444444x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 0.4444444444x + x2 = 12 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 = 12 + 0.04938271604 Reorder the terms: 0.04938271604 + 0.4444444444x + x2 = 12 + 0.04938271604 Combine like terms: 12 + 0.04938271604 = 12.04938271604 0.04938271604 + 0.4444444444x + x2 = 12.04938271604 Factor a perfect square on the left side: (x + 0.2222222222)(x + 0.2222222222) = 12.04938271604 Calculate the square root of the right side: 3.471222078 Break this problem into two subproblems by setting (x + 0.2222222222) equal to 3.471222078 and -3.471222078.Subproblem 1
x + 0.2222222222 = 3.471222078 Simplifying x + 0.2222222222 = 3.471222078 Reorder the terms: 0.2222222222 + x = 3.471222078 Solving 0.2222222222 + x = 3.471222078 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 = 3.471222078 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = 3.471222078 + -0.2222222222 x = 3.471222078 + -0.2222222222 Combine like terms: 3.471222078 + -0.2222222222 = 3.2489998558 x = 3.2489998558 Simplifying x = 3.2489998558Subproblem 2
x + 0.2222222222 = -3.471222078 Simplifying x + 0.2222222222 = -3.471222078 Reorder the terms: 0.2222222222 + x = -3.471222078 Solving 0.2222222222 + x = -3.471222078 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 = -3.471222078 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = -3.471222078 + -0.2222222222 x = -3.471222078 + -0.2222222222 Combine like terms: -3.471222078 + -0.2222222222 = -3.6934443002 x = -3.6934443002 Simplifying x = -3.6934443002Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.2489998558, -3.6934443002}
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