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Simplifying (X + 2) * X = 400 Reorder the terms: (2 + X) * X = 400 Reorder the terms for easier multiplication: X(2 + X) = 400 (2 * X + X * X) = 400 (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 = 19.024984395 X = 19.024984395 Simplifying X = 19.024984395Subproblem 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 = -21.024984395 X = -21.024984395 Simplifying X = -21.024984395Solution
The solution to the problem is based on the solutions from the subproblems. X = {19.024984395, -21.024984395}
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