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Simplifying X2 + 2X = 320 Reorder the terms: 2X + X2 = 320 Solving 2X + X2 = 320 Solving for variable 'X'. Reorder the terms: -320 + 2X + X2 = 320 + -320 Combine like terms: 320 + -320 = 0 -320 + 2X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '320' to each side of the equation. -320 + 2X + 320 + X2 = 0 + 320 Reorder the terms: -320 + 320 + 2X + X2 = 0 + 320 Combine like terms: -320 + 320 = 0 0 + 2X + X2 = 0 + 320 2X + X2 = 0 + 320 Combine like terms: 0 + 320 = 320 2X + X2 = 320 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 = 320 + 1 Reorder the terms: 1 + 2X + X2 = 320 + 1 Combine like terms: 320 + 1 = 321 1 + 2X + X2 = 321 Factor a perfect square on the left side: (X + 1)(X + 1) = 321 Calculate the square root of the right side: 17.916472867 Break this problem into two subproblems by setting (X + 1) equal to 17.916472867 and -17.916472867.Subproblem 1
X + 1 = 17.916472867 Simplifying X + 1 = 17.916472867 Reorder the terms: 1 + X = 17.916472867 Solving 1 + X = 17.916472867 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 = 17.916472867 + -1 Combine like terms: 1 + -1 = 0 0 + X = 17.916472867 + -1 X = 17.916472867 + -1 Combine like terms: 17.916472867 + -1 = 16.916472867 X = 16.916472867 Simplifying X = 16.916472867Subproblem 2
X + 1 = -17.916472867 Simplifying X + 1 = -17.916472867 Reorder the terms: 1 + X = -17.916472867 Solving 1 + X = -17.916472867 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 = -17.916472867 + -1 Combine like terms: 1 + -1 = 0 0 + X = -17.916472867 + -1 X = -17.916472867 + -1 Combine like terms: -17.916472867 + -1 = -18.916472867 X = -18.916472867 Simplifying X = -18.916472867Solution
The solution to the problem is based on the solutions from the subproblems. X = {16.916472867, -18.916472867}
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