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Simplifying 16x2 + 576x + -254571 = 0 Reorder the terms: -254571 + 576x + 16x2 = 0 Solving -254571 + 576x + 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'. -15910.6875 + 36x + x2 = 0 Move the constant term to the right: Add '15910.6875' to each side of the equation. -15910.6875 + 36x + 15910.6875 + x2 = 0 + 15910.6875 Reorder the terms: -15910.6875 + 15910.6875 + 36x + x2 = 0 + 15910.6875 Combine like terms: -15910.6875 + 15910.6875 = 0.0000 0.0000 + 36x + x2 = 0 + 15910.6875 36x + x2 = 0 + 15910.6875 Combine like terms: 0 + 15910.6875 = 15910.6875 36x + x2 = 15910.6875 The x term is 36x. Take half its coefficient (18). Square it (324) and add it to both sides. Add '324' to each side of the equation. 36x + 324 + x2 = 15910.6875 + 324 Reorder the terms: 324 + 36x + x2 = 15910.6875 + 324 Combine like terms: 15910.6875 + 324 = 16234.6875 324 + 36x + x2 = 16234.6875 Factor a perfect square on the left side: (x + 18)(x + 18) = 16234.6875 Calculate the square root of the right side: 127.415413118 Break this problem into two subproblems by setting (x + 18) equal to 127.415413118 and -127.415413118.Subproblem 1
x + 18 = 127.415413118 Simplifying x + 18 = 127.415413118 Reorder the terms: 18 + x = 127.415413118 Solving 18 + x = 127.415413118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = 127.415413118 + -18 Combine like terms: 18 + -18 = 0 0 + x = 127.415413118 + -18 x = 127.415413118 + -18 Combine like terms: 127.415413118 + -18 = 109.415413118 x = 109.415413118 Simplifying x = 109.415413118Subproblem 2
x + 18 = -127.415413118 Simplifying x + 18 = -127.415413118 Reorder the terms: 18 + x = -127.415413118 Solving 18 + x = -127.415413118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = -127.415413118 + -18 Combine like terms: 18 + -18 = 0 0 + x = -127.415413118 + -18 x = -127.415413118 + -18 Combine like terms: -127.415413118 + -18 = -145.415413118 x = -145.415413118 Simplifying x = -145.415413118Solution
The solution to the problem is based on the solutions from the subproblems. x = {109.415413118, -145.415413118}
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