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Simplifying X(X + 1) + (X + 2) = 159 Reorder the terms: X(1 + X) + (X + 2) = 159 (1 * X + X * X) + (X + 2) = 159 (1X + X2) + (X + 2) = 159 Reorder the terms: 1X + X2 + (2 + X) = 159 Remove parenthesis around (2 + X) 1X + X2 + 2 + X = 159 Reorder the terms: 2 + 1X + X + X2 = 159 Combine like terms: 1X + X = 2X 2 + 2X + X2 = 159 Solving 2 + 2X + X2 = 159 Solving for variable 'X'. Reorder the terms: 2 + -159 + 2X + X2 = 159 + -159 Combine like terms: 2 + -159 = -157 -157 + 2X + X2 = 159 + -159 Combine like terms: 159 + -159 = 0 -157 + 2X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '157' to each side of the equation. -157 + 2X + 157 + X2 = 0 + 157 Reorder the terms: -157 + 157 + 2X + X2 = 0 + 157 Combine like terms: -157 + 157 = 0 0 + 2X + X2 = 0 + 157 2X + X2 = 0 + 157 Combine like terms: 0 + 157 = 157 2X + X2 = 157 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 = 157 + 1 Reorder the terms: 1 + 2X + X2 = 157 + 1 Combine like terms: 157 + 1 = 158 1 + 2X + X2 = 158 Factor a perfect square on the left side: (X + 1)(X + 1) = 158 Calculate the square root of the right side: 12.56980509 Break this problem into two subproblems by setting (X + 1) equal to 12.56980509 and -12.56980509.Subproblem 1
X + 1 = 12.56980509 Simplifying X + 1 = 12.56980509 Reorder the terms: 1 + X = 12.56980509 Solving 1 + X = 12.56980509 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 = 12.56980509 + -1 Combine like terms: 1 + -1 = 0 0 + X = 12.56980509 + -1 X = 12.56980509 + -1 Combine like terms: 12.56980509 + -1 = 11.56980509 X = 11.56980509 Simplifying X = 11.56980509Subproblem 2
X + 1 = -12.56980509 Simplifying X + 1 = -12.56980509 Reorder the terms: 1 + X = -12.56980509 Solving 1 + X = -12.56980509 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 = -12.56980509 + -1 Combine like terms: 1 + -1 = 0 0 + X = -12.56980509 + -1 X = -12.56980509 + -1 Combine like terms: -12.56980509 + -1 = -13.56980509 X = -13.56980509 Simplifying X = -13.56980509Solution
The solution to the problem is based on the solutions from the subproblems. X = {11.56980509, -13.56980509}
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