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Simplifying 0 = 3x2 + 111x + 348 Reorder the terms: 0 = 348 + 111x + 3x2 Solving 0 = 348 + 111x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -348 = -348 -348 + -111x + -3x2 = 348 + 111x + 3x2 + -348 + -111x + -3x2 Reorder the terms: -348 + -111x + -3x2 = 348 + -348 + 111x + -111x + 3x2 + -3x2 Combine like terms: 348 + -348 = 0 -348 + -111x + -3x2 = 0 + 111x + -111x + 3x2 + -3x2 -348 + -111x + -3x2 = 111x + -111x + 3x2 + -3x2 Combine like terms: 111x + -111x = 0 -348 + -111x + -3x2 = 0 + 3x2 + -3x2 -348 + -111x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -348 + -111x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(116 + 37x + x2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(116 + 37x + x2)' equal to zero and attempt to solve: Simplifying 116 + 37x + x2 = 0 Solving 116 + 37x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-116' to each side of the equation. 116 + 37x + -116 + x2 = 0 + -116 Reorder the terms: 116 + -116 + 37x + x2 = 0 + -116 Combine like terms: 116 + -116 = 0 0 + 37x + x2 = 0 + -116 37x + x2 = 0 + -116 Combine like terms: 0 + -116 = -116 37x + x2 = -116 The x term is 37x. Take half its coefficient (18.5). Square it (342.25) and add it to both sides. Add '342.25' to each side of the equation. 37x + 342.25 + x2 = -116 + 342.25 Reorder the terms: 342.25 + 37x + x2 = -116 + 342.25 Combine like terms: -116 + 342.25 = 226.25 342.25 + 37x + x2 = 226.25 Factor a perfect square on the left side: (x + 18.5)(x + 18.5) = 226.25 Calculate the square root of the right side: 15.041608956 Break this problem into two subproblems by setting (x + 18.5) equal to 15.041608956 and -15.041608956.Subproblem 1
x + 18.5 = 15.041608956 Simplifying x + 18.5 = 15.041608956 Reorder the terms: 18.5 + x = 15.041608956 Solving 18.5 + x = 15.041608956 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.5' to each side of the equation. 18.5 + -18.5 + x = 15.041608956 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = 15.041608956 + -18.5 x = 15.041608956 + -18.5 Combine like terms: 15.041608956 + -18.5 = -3.458391044 x = -3.458391044 Simplifying x = -3.458391044Subproblem 2
x + 18.5 = -15.041608956 Simplifying x + 18.5 = -15.041608956 Reorder the terms: 18.5 + x = -15.041608956 Solving 18.5 + x = -15.041608956 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.5' to each side of the equation. 18.5 + -18.5 + x = -15.041608956 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = -15.041608956 + -18.5 x = -15.041608956 + -18.5 Combine like terms: -15.041608956 + -18.5 = -33.541608956 x = -33.541608956 Simplifying x = -33.541608956Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.458391044, -33.541608956}Solution
x = {-3.458391044, -33.541608956}
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