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Simplifying (X + 2)(X) = 144 Reorder the terms: (2 + X)(X) = 144 Reorder the terms for easier multiplication: X(2 + X) = 144 (2 * X + X * X) = 144 (2X + X2) = 144 Solving 2X + X2 = 144 Solving for variable 'X'. Reorder the terms: -144 + 2X + X2 = 144 + -144 Combine like terms: 144 + -144 = 0 -144 + 2X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + 2X + 144 + X2 = 0 + 144 Reorder the terms: -144 + 144 + 2X + X2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 2X + X2 = 0 + 144 2X + X2 = 0 + 144 Combine like terms: 0 + 144 = 144 2X + X2 = 144 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 = 144 + 1 Reorder the terms: 1 + 2X + X2 = 144 + 1 Combine like terms: 144 + 1 = 145 1 + 2X + X2 = 145 Factor a perfect square on the left side: (X + 1)(X + 1) = 145 Calculate the square root of the right side: 12.041594579 Break this problem into two subproblems by setting (X + 1) equal to 12.041594579 and -12.041594579.Subproblem 1
X + 1 = 12.041594579 Simplifying X + 1 = 12.041594579 Reorder the terms: 1 + X = 12.041594579 Solving 1 + X = 12.041594579 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 = 12.041594579 + -1 Combine like terms: 1 + -1 = 0 0 + X = 12.041594579 + -1 X = 12.041594579 + -1 Combine like terms: 12.041594579 + -1 = 11.041594579 X = 11.041594579 Simplifying X = 11.041594579Subproblem 2
X + 1 = -12.041594579 Simplifying X + 1 = -12.041594579 Reorder the terms: 1 + X = -12.041594579 Solving 1 + X = -12.041594579 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 = -12.041594579 + -1 Combine like terms: 1 + -1 = 0 0 + X = -12.041594579 + -1 X = -12.041594579 + -1 Combine like terms: -12.041594579 + -1 = -13.041594579 X = -13.041594579 Simplifying X = -13.041594579Solution
The solution to the problem is based on the solutions from the subproblems. X = {11.041594579, -13.041594579}
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