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Simplifying x2 + x = 2014 Reorder the terms: x + x2 = 2014 Solving x + x2 = 2014 Solving for variable 'x'. Reorder the terms: -2014 + x + x2 = 2014 + -2014 Combine like terms: 2014 + -2014 = 0 -2014 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2014' to each side of the equation. -2014 + x + 2014 + x2 = 0 + 2014 Reorder the terms: -2014 + 2014 + x + x2 = 0 + 2014 Combine like terms: -2014 + 2014 = 0 0 + x + x2 = 0 + 2014 x + x2 = 0 + 2014 Combine like terms: 0 + 2014 = 2014 x + x2 = 2014 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. x + 0.25 + x2 = 2014 + 0.25 Reorder the terms: 0.25 + x + x2 = 2014 + 0.25 Combine like terms: 2014 + 0.25 = 2014.25 0.25 + x + x2 = 2014.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2014.25 Calculate the square root of the right side: 44.880396611 Break this problem into two subproblems by setting (x + 0.5) equal to 44.880396611 and -44.880396611.Subproblem 1
x + 0.5 = 44.880396611 Simplifying x + 0.5 = 44.880396611 Reorder the terms: 0.5 + x = 44.880396611 Solving 0.5 + x = 44.880396611 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 = 44.880396611 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 44.880396611 + -0.5 x = 44.880396611 + -0.5 Combine like terms: 44.880396611 + -0.5 = 44.380396611 x = 44.380396611 Simplifying x = 44.380396611Subproblem 2
x + 0.5 = -44.880396611 Simplifying x + 0.5 = -44.880396611 Reorder the terms: 0.5 + x = -44.880396611 Solving 0.5 + x = -44.880396611 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 = -44.880396611 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -44.880396611 + -0.5 x = -44.880396611 + -0.5 Combine like terms: -44.880396611 + -0.5 = -45.380396611 x = -45.380396611 Simplifying x = -45.380396611Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.380396611, -45.380396611}
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