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Simplifying 16x2 + 17x + -39 = 0 Reorder the terms: -39 + 17x + 16x2 = 0 Solving -39 + 17x + 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'. -2.4375 + 1.0625x + x2 = 0 Move the constant term to the right: Add '2.4375' to each side of the equation. -2.4375 + 1.0625x + 2.4375 + x2 = 0 + 2.4375 Reorder the terms: -2.4375 + 2.4375 + 1.0625x + x2 = 0 + 2.4375 Combine like terms: -2.4375 + 2.4375 = 0.0000 0.0000 + 1.0625x + x2 = 0 + 2.4375 1.0625x + x2 = 0 + 2.4375 Combine like terms: 0 + 2.4375 = 2.4375 1.0625x + x2 = 2.4375 The x term is 1.0625x. Take half its coefficient (0.53125). Square it (0.2822265625) and add it to both sides. Add '0.2822265625' to each side of the equation. 1.0625x + 0.2822265625 + x2 = 2.4375 + 0.2822265625 Reorder the terms: 0.2822265625 + 1.0625x + x2 = 2.4375 + 0.2822265625 Combine like terms: 2.4375 + 0.2822265625 = 2.7197265625 0.2822265625 + 1.0625x + x2 = 2.7197265625 Factor a perfect square on the left side: (x + 0.53125)(x + 0.53125) = 2.7197265625 Calculate the square root of the right side: 1.64915935 Break this problem into two subproblems by setting (x + 0.53125) equal to 1.64915935 and -1.64915935.Subproblem 1
x + 0.53125 = 1.64915935 Simplifying x + 0.53125 = 1.64915935 Reorder the terms: 0.53125 + x = 1.64915935 Solving 0.53125 + x = 1.64915935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.53125' to each side of the equation. 0.53125 + -0.53125 + x = 1.64915935 + -0.53125 Combine like terms: 0.53125 + -0.53125 = 0.00000 0.00000 + x = 1.64915935 + -0.53125 x = 1.64915935 + -0.53125 Combine like terms: 1.64915935 + -0.53125 = 1.11790935 x = 1.11790935 Simplifying x = 1.11790935Subproblem 2
x + 0.53125 = -1.64915935 Simplifying x + 0.53125 = -1.64915935 Reorder the terms: 0.53125 + x = -1.64915935 Solving 0.53125 + x = -1.64915935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.53125' to each side of the equation. 0.53125 + -0.53125 + x = -1.64915935 + -0.53125 Combine like terms: 0.53125 + -0.53125 = 0.00000 0.00000 + x = -1.64915935 + -0.53125 x = -1.64915935 + -0.53125 Combine like terms: -1.64915935 + -0.53125 = -2.18040935 x = -2.18040935 Simplifying x = -2.18040935Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.11790935, -2.18040935}
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