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Simplifying 3x2 + x + -166 = 0 Reorder the terms: -166 + x + 3x2 = 0 Solving -166 + x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -55.33333333 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '55.33333333' to each side of the equation. -55.33333333 + 0.3333333333x + 55.33333333 + x2 = 0 + 55.33333333 Reorder the terms: -55.33333333 + 55.33333333 + 0.3333333333x + x2 = 0 + 55.33333333 Combine like terms: -55.33333333 + 55.33333333 = 0.00000000 0.00000000 + 0.3333333333x + x2 = 0 + 55.33333333 0.3333333333x + x2 = 0 + 55.33333333 Combine like terms: 0 + 55.33333333 = 55.33333333 0.3333333333x + x2 = 55.33333333 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333x + 0.25 + x2 = 55.33333333 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = 55.33333333 + 0.25 Combine like terms: 55.33333333 + 0.25 = 55.58333333 0.25 + 0.3333333333x + x2 = 55.58333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 55.58333333 Calculate the square root of the right side: 7.455423082 Break this problem into two subproblems by setting (x + 0.5) equal to 7.455423082 and -7.455423082.Subproblem 1
x + 0.5 = 7.455423082 Simplifying x + 0.5 = 7.455423082 Reorder the terms: 0.5 + x = 7.455423082 Solving 0.5 + x = 7.455423082 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 7.455423082 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 7.455423082 + -0.5 x = 7.455423082 + -0.5 Combine like terms: 7.455423082 + -0.5 = 6.955423082 x = 6.955423082 Simplifying x = 6.955423082Subproblem 2
x + 0.5 = -7.455423082 Simplifying x + 0.5 = -7.455423082 Reorder the terms: 0.5 + x = -7.455423082 Solving 0.5 + x = -7.455423082 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -7.455423082 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -7.455423082 + -0.5 x = -7.455423082 + -0.5 Combine like terms: -7.455423082 + -0.5 = -7.955423082 x = -7.955423082 Simplifying x = -7.955423082Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.955423082, -7.955423082}
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