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Simplifying x2 + x + -6400 = 0 Reorder the terms: -6400 + x + x2 = 0 Solving -6400 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '6400' to each side of the equation. -6400 + x + 6400 + x2 = 0 + 6400 Reorder the terms: -6400 + 6400 + x + x2 = 0 + 6400 Combine like terms: -6400 + 6400 = 0 0 + x + x2 = 0 + 6400 x + x2 = 0 + 6400 Combine like terms: 0 + 6400 = 6400 x + x2 = 6400 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 = 6400 + 0.25 Reorder the terms: 0.25 + x + x2 = 6400 + 0.25 Combine like terms: 6400 + 0.25 = 6400.25 0.25 + x + x2 = 6400.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 6400.25 Calculate the square root of the right side: 80.001562485 Break this problem into two subproblems by setting (x + 0.5) equal to 80.001562485 and -80.001562485.Subproblem 1
x + 0.5 = 80.001562485 Simplifying x + 0.5 = 80.001562485 Reorder the terms: 0.5 + x = 80.001562485 Solving 0.5 + x = 80.001562485 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 = 80.001562485 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 80.001562485 + -0.5 x = 80.001562485 + -0.5 Combine like terms: 80.001562485 + -0.5 = 79.501562485 x = 79.501562485 Simplifying x = 79.501562485Subproblem 2
x + 0.5 = -80.001562485 Simplifying x + 0.5 = -80.001562485 Reorder the terms: 0.5 + x = -80.001562485 Solving 0.5 + x = -80.001562485 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 = -80.001562485 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -80.001562485 + -0.5 x = -80.001562485 + -0.5 Combine like terms: -80.001562485 + -0.5 = -80.501562485 x = -80.501562485 Simplifying x = -80.501562485Solution
The solution to the problem is based on the solutions from the subproblems. x = {79.501562485, -80.501562485}
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