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Simplifying 286 = x + x2 Solving 286 = x + x2 Solving for variable 'x'. Reorder the terms: 286 + -1x + -1x2 = x + -1x + x2 + -1x2 Combine like terms: x + -1x = 0 286 + -1x + -1x2 = 0 + x2 + -1x2 286 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 286 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -286 + x + x2 = 0 Move the constant term to the right: Add '286' to each side of the equation. -286 + x + 286 + x2 = 0 + 286 Reorder the terms: -286 + 286 + x + x2 = 0 + 286 Combine like terms: -286 + 286 = 0 0 + x + x2 = 0 + 286 x + x2 = 0 + 286 Combine like terms: 0 + 286 = 286 x + x2 = 286 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. + 0.25 + x2 = 286 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 286 + 0.25 Combine like terms: 286 + 0.25 = 286.25 1.25 + x2 = 286.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 286.25 Calculate the square root of the right side: 16.918924316 Break this problem into two subproblems by setting (x + 0.5) equal to 16.918924316 and -16.918924316.Subproblem 1
x + 0.5 = 16.918924316 Simplifying x + 0.5 = 16.918924316 Reorder the terms: 0.5 + x = 16.918924316 Solving 0.5 + x = 16.918924316 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 = 16.918924316 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 16.918924316 + -0.5 x = 16.918924316 + -0.5 Combine like terms: 16.918924316 + -0.5 = 16.418924316 x = 16.418924316 Simplifying x = 16.418924316Subproblem 2
x + 0.5 = -16.918924316 Simplifying x + 0.5 = -16.918924316 Reorder the terms: 0.5 + x = -16.918924316 Solving 0.5 + x = -16.918924316 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 = -16.918924316 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -16.918924316 + -0.5 x = -16.918924316 + -0.5 Combine like terms: -16.918924316 + -0.5 = -17.418924316 x = -17.418924316 Simplifying x = -17.418924316Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.418924316, -17.418924316}
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