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Simplifying x2 + x + -1600 = 0 Reorder the terms: -1600 + x + x2 = 0 Solving -1600 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1600' to each side of the equation. -1600 + x + 1600 + x2 = 0 + 1600 Reorder the terms: -1600 + 1600 + x + x2 = 0 + 1600 Combine like terms: -1600 + 1600 = 0 0 + x + x2 = 0 + 1600 x + x2 = 0 + 1600 Combine like terms: 0 + 1600 = 1600 x + x2 = 1600 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 = 1600 + 0.25 Reorder the terms: 0.25 + x + x2 = 1600 + 0.25 Combine like terms: 1600 + 0.25 = 1600.25 0.25 + x + x2 = 1600.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1600.25 Calculate the square root of the right side: 40.003124878 Break this problem into two subproblems by setting (x + 0.5) equal to 40.003124878 and -40.003124878.Subproblem 1
x + 0.5 = 40.003124878 Simplifying x + 0.5 = 40.003124878 Reorder the terms: 0.5 + x = 40.003124878 Solving 0.5 + x = 40.003124878 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 = 40.003124878 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 40.003124878 + -0.5 x = 40.003124878 + -0.5 Combine like terms: 40.003124878 + -0.5 = 39.503124878 x = 39.503124878 Simplifying x = 39.503124878Subproblem 2
x + 0.5 = -40.003124878 Simplifying x + 0.5 = -40.003124878 Reorder the terms: 0.5 + x = -40.003124878 Solving 0.5 + x = -40.003124878 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 = -40.003124878 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -40.003124878 + -0.5 x = -40.003124878 + -0.5 Combine like terms: -40.003124878 + -0.5 = -40.503124878 x = -40.503124878 Simplifying x = -40.503124878Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.503124878, -40.503124878}
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