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Simplifying x2 + 2x + -6400 = 0 Reorder the terms: -6400 + 2x + x2 = 0 Solving -6400 + 2x + 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 + 2x + 6400 + x2 = 0 + 6400 Reorder the terms: -6400 + 6400 + 2x + x2 = 0 + 6400 Combine like terms: -6400 + 6400 = 0 0 + 2x + x2 = 0 + 6400 2x + x2 = 0 + 6400 Combine like terms: 0 + 6400 = 6400 2x + x2 = 6400 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 = 6400 + 1 Reorder the terms: 1 + 2x + x2 = 6400 + 1 Combine like terms: 6400 + 1 = 6401 1 + 2x + x2 = 6401 Factor a perfect square on the left side: (x + 1)(x + 1) = 6401 Calculate the square root of the right side: 80.006249756 Break this problem into two subproblems by setting (x + 1) equal to 80.006249756 and -80.006249756.Subproblem 1
x + 1 = 80.006249756 Simplifying x + 1 = 80.006249756 Reorder the terms: 1 + x = 80.006249756 Solving 1 + x = 80.006249756 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 = 80.006249756 + -1 Combine like terms: 1 + -1 = 0 0 + x = 80.006249756 + -1 x = 80.006249756 + -1 Combine like terms: 80.006249756 + -1 = 79.006249756 x = 79.006249756 Simplifying x = 79.006249756Subproblem 2
x + 1 = -80.006249756 Simplifying x + 1 = -80.006249756 Reorder the terms: 1 + x = -80.006249756 Solving 1 + x = -80.006249756 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 = -80.006249756 + -1 Combine like terms: 1 + -1 = 0 0 + x = -80.006249756 + -1 x = -80.006249756 + -1 Combine like terms: -80.006249756 + -1 = -81.006249756 x = -81.006249756 Simplifying x = -81.006249756Solution
The solution to the problem is based on the solutions from the subproblems. x = {79.006249756, -81.006249756}
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