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Simplifying x + -16 + 272 = x2 Reorder the terms: -16 + 272 + x = x2 Combine like terms: -16 + 272 = 256 256 + x = x2 Solving 256 + x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 256 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -256 + -1x + x2 = 0 Move the constant term to the right: Add '256' to each side of the equation. -256 + -1x + 256 + x2 = 0 + 256 Reorder the terms: -256 + 256 + -1x + x2 = 0 + 256 Combine like terms: -256 + 256 = 0 0 + -1x + x2 = 0 + 256 -1x + x2 = 0 + 256 Combine like terms: 0 + 256 = 256 -1x + x2 = 256 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 256 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 256 + 0.25 Combine like terms: 256 + 0.25 = 256.25 0.25 + -1x + x2 = 256.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 256.25 Calculate the square root of the right side: 16.007810594 Break this problem into two subproblems by setting (x + 0.5) equal to 16.007810594 and -16.007810594.Subproblem 1
x + 0.5 = 16.007810594 Simplifying x + 0.5 = 16.007810594 Reorder the terms: 0.5 + x = 16.007810594 Solving 0.5 + x = 16.007810594 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 16.007810594 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 16.007810594 + -0.5 x = 16.007810594 + -0.5 Combine like terms: 16.007810594 + -0.5 = 15.507810594 x = 15.507810594 Simplifying x = 15.507810594Subproblem 2
x + 0.5 = -16.007810594 Simplifying x + 0.5 = -16.007810594 Reorder the terms: 0.5 + x = -16.007810594 Solving 0.5 + x = -16.007810594 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -16.007810594 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -16.007810594 + -0.5 x = -16.007810594 + -0.5 Combine like terms: -16.007810594 + -0.5 = -16.507810594 x = -16.507810594 Simplifying x = -16.507810594Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.507810594, -16.507810594}
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