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Simplifying 16x2 + -17x + -5 = 0 Reorder the terms: -5 + -17x + 16x2 = 0 Solving -5 + -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'. -0.3125 + -1.0625x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -1.0625x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -1.0625x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -1.0625x + x2 = 0 + 0.3125 -1.0625x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -1.0625x + x2 = 0.3125 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 = 0.3125 + 0.2822265625 Reorder the terms: 0.2822265625 + -1.0625x + x2 = 0.3125 + 0.2822265625 Combine like terms: 0.3125 + 0.2822265625 = 0.5947265625 0.2822265625 + -1.0625x + x2 = 0.5947265625 Factor a perfect square on the left side: (x + -0.53125)(x + -0.53125) = 0.5947265625 Calculate the square root of the right side: 0.771185167 Break this problem into two subproblems by setting (x + -0.53125) equal to 0.771185167 and -0.771185167.Subproblem 1
x + -0.53125 = 0.771185167 Simplifying x + -0.53125 = 0.771185167 Reorder the terms: -0.53125 + x = 0.771185167 Solving -0.53125 + x = 0.771185167 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 = 0.771185167 + 0.53125 Combine like terms: -0.53125 + 0.53125 = 0.00000 0.00000 + x = 0.771185167 + 0.53125 x = 0.771185167 + 0.53125 Combine like terms: 0.771185167 + 0.53125 = 1.302435167 x = 1.302435167 Simplifying x = 1.302435167Subproblem 2
x + -0.53125 = -0.771185167 Simplifying x + -0.53125 = -0.771185167 Reorder the terms: -0.53125 + x = -0.771185167 Solving -0.53125 + x = -0.771185167 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 = -0.771185167 + 0.53125 Combine like terms: -0.53125 + 0.53125 = 0.00000 0.00000 + x = -0.771185167 + 0.53125 x = -0.771185167 + 0.53125 Combine like terms: -0.771185167 + 0.53125 = -0.239935167 x = -0.239935167 Simplifying x = -0.239935167Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.302435167, -0.239935167}
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