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Simplifying x2 + 2x + -2014 = 0 Reorder the terms: -2014 + 2x + x2 = 0 Solving -2014 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2014' to each side of the equation. -2014 + 2x + 2014 + x2 = 0 + 2014 Reorder the terms: -2014 + 2014 + 2x + x2 = 0 + 2014 Combine like terms: -2014 + 2014 = 0 0 + 2x + x2 = 0 + 2014 2x + x2 = 0 + 2014 Combine like terms: 0 + 2014 = 2014 2x + x2 = 2014 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 = 2014 + 1 Reorder the terms: 1 + 2x + x2 = 2014 + 1 Combine like terms: 2014 + 1 = 2015 1 + 2x + x2 = 2015 Factor a perfect square on the left side: (x + 1)(x + 1) = 2015 Calculate the square root of the right side: 44.888751375 Break this problem into two subproblems by setting (x + 1) equal to 44.888751375 and -44.888751375.Subproblem 1
x + 1 = 44.888751375 Simplifying x + 1 = 44.888751375 Reorder the terms: 1 + x = 44.888751375 Solving 1 + x = 44.888751375 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 = 44.888751375 + -1 Combine like terms: 1 + -1 = 0 0 + x = 44.888751375 + -1 x = 44.888751375 + -1 Combine like terms: 44.888751375 + -1 = 43.888751375 x = 43.888751375 Simplifying x = 43.888751375Subproblem 2
x + 1 = -44.888751375 Simplifying x + 1 = -44.888751375 Reorder the terms: 1 + x = -44.888751375 Solving 1 + x = -44.888751375 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 = -44.888751375 + -1 Combine like terms: 1 + -1 = 0 0 + x = -44.888751375 + -1 x = -44.888751375 + -1 Combine like terms: -44.888751375 + -1 = -45.888751375 x = -45.888751375 Simplifying x = -45.888751375Solution
The solution to the problem is based on the solutions from the subproblems. x = {43.888751375, -45.888751375}
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