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Simplifying 2x2 + 21x + -162 = 0 Reorder the terms: -162 + 21x + 2x2 = 0 Solving -162 + 21x + 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 + 10.5x + x2 = 0 Move the constant term to the right: Add '81' to each side of the equation. -81 + 10.5x + 81 + x2 = 0 + 81 Reorder the terms: -81 + 81 + 10.5x + x2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + 10.5x + x2 = 0 + 81 10.5x + x2 = 0 + 81 Combine like terms: 0 + 81 = 81 10.5x + x2 = 81 The x term is 10.5x. Take half its coefficient (5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. 10.5x + 27.5625 + x2 = 81 + 27.5625 Reorder the terms: 27.5625 + 10.5x + x2 = 81 + 27.5625 Combine like terms: 81 + 27.5625 = 108.5625 27.5625 + 10.5x + x2 = 108.5625 Factor a perfect square on the left side: (x + 5.25)(x + 5.25) = 108.5625 Calculate the square root of the right side: 10.419332992 Break this problem into two subproblems by setting (x + 5.25) equal to 10.419332992 and -10.419332992.Subproblem 1
x + 5.25 = 10.419332992 Simplifying x + 5.25 = 10.419332992 Reorder the terms: 5.25 + x = 10.419332992 Solving 5.25 + x = 10.419332992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = 10.419332992 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 10.419332992 + -5.25 x = 10.419332992 + -5.25 Combine like terms: 10.419332992 + -5.25 = 5.169332992 x = 5.169332992 Simplifying x = 5.169332992Subproblem 2
x + 5.25 = -10.419332992 Simplifying x + 5.25 = -10.419332992 Reorder the terms: 5.25 + x = -10.419332992 Solving 5.25 + x = -10.419332992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = -10.419332992 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -10.419332992 + -5.25 x = -10.419332992 + -5.25 Combine like terms: -10.419332992 + -5.25 = -15.669332992 x = -15.669332992 Simplifying x = -15.669332992Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.169332992, -15.669332992}
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