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Simplifying 16x2 + 17x + -4 = 0 Reorder the terms: -4 + 17x + 16x2 = 0 Solving -4 + 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'. -0.25 + 1.0625x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 1.0625x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 1.0625x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 1.0625x + x2 = 0 + 0.25 1.0625x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 1.0625x + x2 = 0.25 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 = 0.25 + 0.2822265625 Reorder the terms: 0.2822265625 + 1.0625x + x2 = 0.25 + 0.2822265625 Combine like terms: 0.25 + 0.2822265625 = 0.5322265625 0.2822265625 + 1.0625x + x2 = 0.5322265625 Factor a perfect square on the left side: (x + 0.53125)(x + 0.53125) = 0.5322265625 Calculate the square root of the right side: 0.729538596 Break this problem into two subproblems by setting (x + 0.53125) equal to 0.729538596 and -0.729538596.Subproblem 1
x + 0.53125 = 0.729538596 Simplifying x + 0.53125 = 0.729538596 Reorder the terms: 0.53125 + x = 0.729538596 Solving 0.53125 + x = 0.729538596 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 = 0.729538596 + -0.53125 Combine like terms: 0.53125 + -0.53125 = 0.00000 0.00000 + x = 0.729538596 + -0.53125 x = 0.729538596 + -0.53125 Combine like terms: 0.729538596 + -0.53125 = 0.198288596 x = 0.198288596 Simplifying x = 0.198288596Subproblem 2
x + 0.53125 = -0.729538596 Simplifying x + 0.53125 = -0.729538596 Reorder the terms: 0.53125 + x = -0.729538596 Solving 0.53125 + x = -0.729538596 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 = -0.729538596 + -0.53125 Combine like terms: 0.53125 + -0.53125 = 0.00000 0.00000 + x = -0.729538596 + -0.53125 x = -0.729538596 + -0.53125 Combine like terms: -0.729538596 + -0.53125 = -1.260788596 x = -1.260788596 Simplifying x = -1.260788596Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.198288596, -1.260788596}
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