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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 = 25.0625 25 + -10X + X2 = 25.0625 Factor a perfect square on the left side: (X + -5)(X + -5) = 25.0625 Calculate the square root of the right side: 5.006246099 Break this problem into two subproblems by setting (X + -5) equal to 5.006246099 and -5.006246099.Subproblem 1
X + -5 = 5.006246099 Simplifying X + -5 = 5.006246099 Reorder the terms: -5 + X = 5.006246099 Solving -5 + X = 5.006246099 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 = 5.006246099 + 5 Combine like terms: -5 + 5 = 0 0 + X = 5.006246099 + 5 X = 5.006246099 + 5 Combine like terms: 5.006246099 + 5 = 10.006246099 X = 10.006246099 Simplifying X = 10.006246099Subproblem 2
X + -5 = -5.006246099 Simplifying X + -5 = -5.006246099 Reorder the terms: -5 + X = -5.006246099 Solving -5 + X = -5.006246099 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 = -5.006246099 + 5 Combine like terms: -5 + 5 = 0 0 + X = -5.006246099 + 5 X = -5.006246099 + 5 Combine like terms: -5.006246099 + 5 = -0.006246099 X = -0.006246099 Simplifying X = -0.006246099Solution
The solution to the problem is based on the solutions from the subproblems. X = {10.006246099, -0.006246099}
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