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Simplifying 0 = x2 + -256 + -1x + -14 Reorder the terms: 0 = -256 + -14 + -1x + x2 Combine like terms: -256 + -14 = -270 0 = -270 + -1x + x2 Solving 0 = -270 + -1x + x2 Solving for variable 'x'. Combine like terms: 0 + 270 = 270 270 + x + -1x2 = -270 + -1x + x2 + 270 + x + -1x2 Reorder the terms: 270 + x + -1x2 = -270 + 270 + -1x + x + x2 + -1x2 Combine like terms: -270 + 270 = 0 270 + x + -1x2 = 0 + -1x + x + x2 + -1x2 270 + x + -1x2 = -1x + x + x2 + -1x2 Combine like terms: -1x + x = 0 270 + x + -1x2 = 0 + x2 + -1x2 270 + x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 270 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -270 + -1x + x2 = 0 Move the constant term to the right: Add '270' to each side of the equation. -270 + -1x + 270 + x2 = 0 + 270 Reorder the terms: -270 + 270 + -1x + x2 = 0 + 270 Combine like terms: -270 + 270 = 0 0 + -1x + x2 = 0 + 270 -1x + x2 = 0 + 270 Combine like terms: 0 + 270 = 270 -1x + x2 = 270 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 = 270 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 270 + 0.25 Combine like terms: 270 + 0.25 = 270.25 0.25 + -1x + x2 = 270.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 270.25 Calculate the square root of the right side: 16.439282223 Break this problem into two subproblems by setting (x + 0.5) equal to 16.439282223 and -16.439282223.Subproblem 1
x + 0.5 = 16.439282223 Simplifying x + 0.5 = 16.439282223 Reorder the terms: 0.5 + x = 16.439282223 Solving 0.5 + x = 16.439282223 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 = 16.439282223 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 16.439282223 + -0.5 x = 16.439282223 + -0.5 Combine like terms: 16.439282223 + -0.5 = 15.939282223 x = 15.939282223 Simplifying x = 15.939282223Subproblem 2
x + 0.5 = -16.439282223 Simplifying x + 0.5 = -16.439282223 Reorder the terms: 0.5 + x = -16.439282223 Solving 0.5 + x = -16.439282223 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 = -16.439282223 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -16.439282223 + -0.5 x = -16.439282223 + -0.5 Combine like terms: -16.439282223 + -0.5 = -16.939282223 x = -16.939282223 Simplifying x = -16.939282223Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.939282223, -16.939282223}
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