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Simplifying 16x2 + 73x + 81 = 0 Reorder the terms: 81 + 73x + 16x2 = 0 Solving 81 + 73x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 5.0625 + 4.5625x + x2 = 0 Move the constant term to the right: Add '-5.0625' to each side of the equation. 5.0625 + 4.5625x + -5.0625 + x2 = 0 + -5.0625 Reorder the terms: 5.0625 + -5.0625 + 4.5625x + x2 = 0 + -5.0625 Combine like terms: 5.0625 + -5.0625 = 0.0000 0.0000 + 4.5625x + x2 = 0 + -5.0625 4.5625x + x2 = 0 + -5.0625 Combine like terms: 0 + -5.0625 = -5.0625 4.5625x + x2 = -5.0625 The x term is 4.5625x. Take half its coefficient (2.28125). Square it (5.204101563) and add it to both sides. Add '5.204101563' to each side of the equation. 4.5625x + 5.204101563 + x2 = -5.0625 + 5.204101563 Reorder the terms: 5.204101563 + 4.5625x + x2 = -5.0625 + 5.204101563 Combine like terms: -5.0625 + 5.204101563 = 0.141601563 5.204101563 + 4.5625x + x2 = 0.141601563 Factor a perfect square on the left side: (x + 2.28125)(x + 2.28125) = 0.141601563 Calculate the square root of the right side: 0.376299831 Break this problem into two subproblems by setting (x + 2.28125) equal to 0.376299831 and -0.376299831.Subproblem 1
x + 2.28125 = 0.376299831 Simplifying x + 2.28125 = 0.376299831 Reorder the terms: 2.28125 + x = 0.376299831 Solving 2.28125 + x = 0.376299831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.28125' to each side of the equation. 2.28125 + -2.28125 + x = 0.376299831 + -2.28125 Combine like terms: 2.28125 + -2.28125 = 0.00000 0.00000 + x = 0.376299831 + -2.28125 x = 0.376299831 + -2.28125 Combine like terms: 0.376299831 + -2.28125 = -1.904950169 x = -1.904950169 Simplifying x = -1.904950169Subproblem 2
x + 2.28125 = -0.376299831 Simplifying x + 2.28125 = -0.376299831 Reorder the terms: 2.28125 + x = -0.376299831 Solving 2.28125 + x = -0.376299831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.28125' to each side of the equation. 2.28125 + -2.28125 + x = -0.376299831 + -2.28125 Combine like terms: 2.28125 + -2.28125 = 0.00000 0.00000 + x = -0.376299831 + -2.28125 x = -0.376299831 + -2.28125 Combine like terms: -0.376299831 + -2.28125 = -2.657549831 x = -2.657549831 Simplifying x = -2.657549831Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.904950169, -2.657549831}
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