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Simplifying (x2 + 2x + -286) = 0 Reorder the terms: (-286 + 2x + x2) = 0 Remove parenthesis around (-286 + 2x + x2) -286 + 2x + x2 = 0 Solving -286 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '286' to each side of the equation. -286 + 2x + 286 + x2 = 0 + 286 Reorder the terms: -286 + 286 + 2x + x2 = 0 + 286 Combine like terms: -286 + 286 = 0 0 + 2x + x2 = 0 + 286 2x + x2 = 0 + 286 Combine like terms: 0 + 286 = 286 2x + x2 = 286 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 286 + 1 Reorder the terms: 1 + 2x + x2 = 286 + 1 Combine like terms: 286 + 1 = 287 1 + 2x + x2 = 287 Factor a perfect square on the left side: (x + 1)(x + 1) = 287 Calculate the square root of the right side: 16.941074346 Break this problem into two subproblems by setting (x + 1) equal to 16.941074346 and -16.941074346.Subproblem 1
x + 1 = 16.941074346 Simplifying x + 1 = 16.941074346 Reorder the terms: 1 + x = 16.941074346 Solving 1 + x = 16.941074346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 16.941074346 + -1 Combine like terms: 1 + -1 = 0 0 + x = 16.941074346 + -1 x = 16.941074346 + -1 Combine like terms: 16.941074346 + -1 = 15.941074346 x = 15.941074346 Simplifying x = 15.941074346Subproblem 2
x + 1 = -16.941074346 Simplifying x + 1 = -16.941074346 Reorder the terms: 1 + x = -16.941074346 Solving 1 + x = -16.941074346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -16.941074346 + -1 Combine like terms: 1 + -1 = 0 0 + x = -16.941074346 + -1 x = -16.941074346 + -1 Combine like terms: -16.941074346 + -1 = -17.941074346 x = -17.941074346 Simplifying x = -17.941074346Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.941074346, -17.941074346}
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