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Simplifying x2 + -2x = 400 Reorder the terms: -2x + x2 = 400 Solving -2x + x2 = 400 Solving for variable 'x'. Reorder the terms: -400 + -2x + x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -400 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + -2x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + -2x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + -2x + x2 = 0 + 400 -2x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 -2x + x2 = 400 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 = 400 + 1 Reorder the terms: 1 + -2x + x2 = 400 + 1 Combine like terms: 400 + 1 = 401 1 + -2x + x2 = 401 Factor a perfect square on the left side: (x + -1)(x + -1) = 401 Calculate the square root of the right side: 20.024984395 Break this problem into two subproblems by setting (x + -1) equal to 20.024984395 and -20.024984395.Subproblem 1
x + -1 = 20.024984395 Simplifying x + -1 = 20.024984395 Reorder the terms: -1 + x = 20.024984395 Solving -1 + x = 20.024984395 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 = 20.024984395 + 1 Combine like terms: -1 + 1 = 0 0 + x = 20.024984395 + 1 x = 20.024984395 + 1 Combine like terms: 20.024984395 + 1 = 21.024984395 x = 21.024984395 Simplifying x = 21.024984395Subproblem 2
x + -1 = -20.024984395 Simplifying x + -1 = -20.024984395 Reorder the terms: -1 + x = -20.024984395 Solving -1 + x = -20.024984395 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 = -20.024984395 + 1 Combine like terms: -1 + 1 = 0 0 + x = -20.024984395 + 1 x = -20.024984395 + 1 Combine like terms: -20.024984395 + 1 = -19.024984395 x = -19.024984395 Simplifying x = -19.024984395Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.024984395, -19.024984395}
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