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Simplifying x2 + 2x = 2015 Reorder the terms: 2x + x2 = 2015 Solving 2x + x2 = 2015 Solving for variable 'x'. Reorder the terms: -2015 + 2x + x2 = 2015 + -2015 Combine like terms: 2015 + -2015 = 0 -2015 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2015' to each side of the equation. -2015 + 2x + 2015 + x2 = 0 + 2015 Reorder the terms: -2015 + 2015 + 2x + x2 = 0 + 2015 Combine like terms: -2015 + 2015 = 0 0 + 2x + x2 = 0 + 2015 2x + x2 = 0 + 2015 Combine like terms: 0 + 2015 = 2015 2x + x2 = 2015 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 = 2015 + 1 Reorder the terms: 1 + 2x + x2 = 2015 + 1 Combine like terms: 2015 + 1 = 2016 1 + 2x + x2 = 2016 Factor a perfect square on the left side: (x + 1)(x + 1) = 2016 Calculate the square root of the right side: 44.899888641 Break this problem into two subproblems by setting (x + 1) equal to 44.899888641 and -44.899888641.Subproblem 1
x + 1 = 44.899888641 Simplifying x + 1 = 44.899888641 Reorder the terms: 1 + x = 44.899888641 Solving 1 + x = 44.899888641 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 = 44.899888641 + -1 Combine like terms: 1 + -1 = 0 0 + x = 44.899888641 + -1 x = 44.899888641 + -1 Combine like terms: 44.899888641 + -1 = 43.899888641 x = 43.899888641 Simplifying x = 43.899888641Subproblem 2
x + 1 = -44.899888641 Simplifying x + 1 = -44.899888641 Reorder the terms: 1 + x = -44.899888641 Solving 1 + x = -44.899888641 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 = -44.899888641 + -1 Combine like terms: 1 + -1 = 0 0 + x = -44.899888641 + -1 x = -44.899888641 + -1 Combine like terms: -44.899888641 + -1 = -45.899888641 x = -45.899888641 Simplifying x = -45.899888641Solution
The solution to the problem is based on the solutions from the subproblems. x = {43.899888641, -45.899888641}
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