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Simplifying 2x2 + -23x + -162 = 0 Reorder the terms: -162 + -23x + 2x2 = 0 Solving -162 + -23x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -81 + -11.5x + x2 = 0 Move the constant term to the right: Add '81' to each side of the equation. -81 + -11.5x + 81 + x2 = 0 + 81 Reorder the terms: -81 + 81 + -11.5x + x2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + -11.5x + x2 = 0 + 81 -11.5x + x2 = 0 + 81 Combine like terms: 0 + 81 = 81 -11.5x + x2 = 81 The x term is -11.5x. Take half its coefficient (-5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. -11.5x + 33.0625 + x2 = 81 + 33.0625 Reorder the terms: 33.0625 + -11.5x + x2 = 81 + 33.0625 Combine like terms: 81 + 33.0625 = 114.0625 33.0625 + -11.5x + x2 = 114.0625 Factor a perfect square on the left side: (x + -5.75)(x + -5.75) = 114.0625 Calculate the square root of the right side: 10.680004682 Break this problem into two subproblems by setting (x + -5.75) equal to 10.680004682 and -10.680004682.Subproblem 1
x + -5.75 = 10.680004682 Simplifying x + -5.75 = 10.680004682 Reorder the terms: -5.75 + x = 10.680004682 Solving -5.75 + x = 10.680004682 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = 10.680004682 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = 10.680004682 + 5.75 x = 10.680004682 + 5.75 Combine like terms: 10.680004682 + 5.75 = 16.430004682 x = 16.430004682 Simplifying x = 16.430004682Subproblem 2
x + -5.75 = -10.680004682 Simplifying x + -5.75 = -10.680004682 Reorder the terms: -5.75 + x = -10.680004682 Solving -5.75 + x = -10.680004682 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = -10.680004682 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = -10.680004682 + 5.75 x = -10.680004682 + 5.75 Combine like terms: -10.680004682 + 5.75 = -4.930004682 x = -4.930004682 Simplifying x = -4.930004682Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.430004682, -4.930004682}
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