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Simplifying 16x2 + -114x = -1 Reorder the terms: -114x + 16x2 = -1 Solving -114x + 16x2 = -1 Solving for variable 'x'. Reorder the terms: 1 + -114x + 16x2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + -114x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.0625 + -7.125x + x2 = 0 Move the constant term to the right: Add '-0.0625' to each side of the equation. 0.0625 + -7.125x + -0.0625 + x2 = 0 + -0.0625 Reorder the terms: 0.0625 + -0.0625 + -7.125x + x2 = 0 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + -7.125x + x2 = 0 + -0.0625 -7.125x + x2 = 0 + -0.0625 Combine like terms: 0 + -0.0625 = -0.0625 -7.125x + x2 = -0.0625 The x term is -7.125x. Take half its coefficient (-3.5625). Square it (12.69140625) and add it to both sides. Add '12.69140625' to each side of the equation. -7.125x + 12.69140625 + x2 = -0.0625 + 12.69140625 Reorder the terms: 12.69140625 + -7.125x + x2 = -0.0625 + 12.69140625 Combine like terms: -0.0625 + 12.69140625 = 12.62890625 12.69140625 + -7.125x + x2 = 12.62890625 Factor a perfect square on the left side: (x + -3.5625)(x + -3.5625) = 12.62890625 Calculate the square root of the right side: 3.553717244 Break this problem into two subproblems by setting (x + -3.5625) equal to 3.553717244 and -3.553717244.Subproblem 1
x + -3.5625 = 3.553717244 Simplifying x + -3.5625 = 3.553717244 Reorder the terms: -3.5625 + x = 3.553717244 Solving -3.5625 + x = 3.553717244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5625' to each side of the equation. -3.5625 + 3.5625 + x = 3.553717244 + 3.5625 Combine like terms: -3.5625 + 3.5625 = 0.0000 0.0000 + x = 3.553717244 + 3.5625 x = 3.553717244 + 3.5625 Combine like terms: 3.553717244 + 3.5625 = 7.116217244 x = 7.116217244 Simplifying x = 7.116217244Subproblem 2
x + -3.5625 = -3.553717244 Simplifying x + -3.5625 = -3.553717244 Reorder the terms: -3.5625 + x = -3.553717244 Solving -3.5625 + x = -3.553717244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5625' to each side of the equation. -3.5625 + 3.5625 + x = -3.553717244 + 3.5625 Combine like terms: -3.5625 + 3.5625 = 0.0000 0.0000 + x = -3.553717244 + 3.5625 x = -3.553717244 + 3.5625 Combine like terms: -3.553717244 + 3.5625 = 0.008782756 x = 0.008782756 Simplifying x = 0.008782756Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.116217244, 0.008782756}
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