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Simplifying 16x2 + 17x + -272 = 0 Reorder the terms: -272 + 17x + 16x2 = 0 Solving -272 + 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'. -17 + 1.0625x + x2 = 0 Move the constant term to the right: Add '17' to each side of the equation. -17 + 1.0625x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + 1.0625x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 1.0625x + x2 = 0 + 17 1.0625x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 1.0625x + x2 = 17 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 = 17 + 0.2822265625 Reorder the terms: 0.2822265625 + 1.0625x + x2 = 17 + 0.2822265625 Combine like terms: 17 + 0.2822265625 = 17.2822265625 0.2822265625 + 1.0625x + x2 = 17.2822265625 Factor a perfect square on the left side: (x + 0.53125)(x + 0.53125) = 17.2822265625 Calculate the square root of the right side: 4.157189743 Break this problem into two subproblems by setting (x + 0.53125) equal to 4.157189743 and -4.157189743.Subproblem 1
x + 0.53125 = 4.157189743 Simplifying x + 0.53125 = 4.157189743 Reorder the terms: 0.53125 + x = 4.157189743 Solving 0.53125 + x = 4.157189743 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 = 4.157189743 + -0.53125 Combine like terms: 0.53125 + -0.53125 = 0.00000 0.00000 + x = 4.157189743 + -0.53125 x = 4.157189743 + -0.53125 Combine like terms: 4.157189743 + -0.53125 = 3.625939743 x = 3.625939743 Simplifying x = 3.625939743Subproblem 2
x + 0.53125 = -4.157189743 Simplifying x + 0.53125 = -4.157189743 Reorder the terms: 0.53125 + x = -4.157189743 Solving 0.53125 + x = -4.157189743 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 = -4.157189743 + -0.53125 Combine like terms: 0.53125 + -0.53125 = 0.00000 0.00000 + x = -4.157189743 + -0.53125 x = -4.157189743 + -0.53125 Combine like terms: -4.157189743 + -0.53125 = -4.688439743 x = -4.688439743 Simplifying x = -4.688439743Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.625939743, -4.688439743}
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