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Simplifying 1 = -16x2 + 160x Reorder the terms: 1 = 160x + -16x2 Solving 1 = 160x + -16x2 Solving for variable 'x'. Reorder the terms: 1 + -160x + 16x2 = 160x + -160x + -16x2 + 16x2 Combine like terms: 160x + -160x = 0 1 + -160x + 16x2 = 0 + -16x2 + 16x2 1 + -160x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 1 + -160x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.0625 + -10x + x2 = 0 Move the constant term to the right: Add '-0.0625' to each side of the equation. 0.0625 + -10x + -0.0625 + x2 = 0 + -0.0625 Reorder the terms: 0.0625 + -0.0625 + -10x + x2 = 0 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + -10x + x2 = 0 + -0.0625 -10x + x2 = 0 + -0.0625 Combine like terms: 0 + -0.0625 = -0.0625 -10x + x2 = -0.0625 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -0.0625 + 25 Reorder the terms: 25 + -10x + x2 = -0.0625 + 25 Combine like terms: -0.0625 + 25 = 24.9375 25 + -10x + x2 = 24.9375 Factor a perfect square on the left side: (x + -5)(x + -5) = 24.9375 Calculate the square root of the right side: 4.993746089 Break this problem into two subproblems by setting (x + -5) equal to 4.993746089 and -4.993746089.Subproblem 1
x + -5 = 4.993746089 Simplifying x + -5 = 4.993746089 Reorder the terms: -5 + x = 4.993746089 Solving -5 + x = 4.993746089 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 4.993746089 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.993746089 + 5 x = 4.993746089 + 5 Combine like terms: 4.993746089 + 5 = 9.993746089 x = 9.993746089 Simplifying x = 9.993746089Subproblem 2
x + -5 = -4.993746089 Simplifying x + -5 = -4.993746089 Reorder the terms: -5 + x = -4.993746089 Solving -5 + x = -4.993746089 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -4.993746089 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.993746089 + 5 x = -4.993746089 + 5 Combine like terms: -4.993746089 + 5 = 0.006253911 x = 0.006253911 Simplifying x = 0.006253911Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.993746089, 0.006253911}
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