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Simplifying 2x2 + (6x) + -183 = 0 Reorder the terms: -183 + (6x) + 2x2 = 0 Solving -183 + (6x) + 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'. -91.5 + (3x) + x2 = 0 Move the constant term to the right: Add '91.5' to each side of the equation. -91.5 + (3x) + 91.5 + x2 = 0 + 91.5 Reorder the terms: -91.5 + 91.5 + (3x) + x2 = 0 + 91.5 Combine like terms: -91.5 + 91.5 = 0.0 0.0 + (3x) + x2 = 0 + 91.5 (3x) + x2 = 0 + 91.5 Combine like terms: 0 + 91.5 = 91.5 (3x) + x2 = 91.5 The x term is (3x). Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. (3x) + 2.25 + x2 = 91.5 + 2.25 Reorder the terms: 2.25 + (3x) + x2 = 91.5 + 2.25 Combine like terms: 91.5 + 2.25 = 93.75 2.25 + (3x) + x2 = 93.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 93.75 Calculate the square root of the right side: 9.682458366 Break this problem into two subproblems by setting (x + 1.5) equal to 9.682458366 and -9.682458366.Subproblem 1
x + 1.5 = 9.682458366 Simplifying x + 1.5 = 9.682458366 Reorder the terms: 1.5 + x = 9.682458366 Solving 1.5 + x = 9.682458366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 9.682458366 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 9.682458366 + -1.5 x = 9.682458366 + -1.5 Combine like terms: 9.682458366 + -1.5 = 8.182458366 x = 8.182458366 Simplifying x = 8.182458366Subproblem 2
x + 1.5 = -9.682458366 Simplifying x + 1.5 = -9.682458366 Reorder the terms: 1.5 + x = -9.682458366 Solving 1.5 + x = -9.682458366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -9.682458366 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -9.682458366 + -1.5 x = -9.682458366 + -1.5 Combine like terms: -9.682458366 + -1.5 = -11.182458366 x = -11.182458366 Simplifying x = -11.182458366Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.182458366, -11.182458366}
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