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Simplifying (X + -1) + [X(X + 1) + -7] = 9 Reorder the terms: (-1 + X) + [X(X + 1) + -7] = 9 Remove parenthesis around (-1 + X) -1 + X + [X(X + 1) + -7] = 9 Reorder the terms: -1 + X + [X(1 + X) + -7] = 9 -1 + X + [(1 * X + X * X) + -7] = 9 -1 + X + [(1X + X2) + -7] = 9 Reorder the terms: -1 + X + [-7 + 1X + X2] = 9 Remove brackets around [-7 + 1X + X2] -1 + X + -7 + 1X + X2 = 9 Reorder the terms: -1 + -7 + X + 1X + X2 = 9 Combine like terms: -1 + -7 = -8 -8 + X + 1X + X2 = 9 Combine like terms: X + 1X = 2X -8 + 2X + X2 = 9 Solving -8 + 2X + X2 = 9 Solving for variable 'X'. Reorder the terms: -8 + -9 + 2X + X2 = 9 + -9 Combine like terms: -8 + -9 = -17 -17 + 2X + X2 = 9 + -9 Combine like terms: 9 + -9 = 0 -17 + 2X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + 2X + 17 + X2 = 0 + 17 Reorder the terms: -17 + 17 + 2X + X2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 2X + X2 = 0 + 17 2X + X2 = 0 + 17 Combine like terms: 0 + 17 = 17 2X + X2 = 17 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 = 17 + 1 Reorder the terms: 1 + 2X + X2 = 17 + 1 Combine like terms: 17 + 1 = 18 1 + 2X + X2 = 18 Factor a perfect square on the left side: (X + 1)(X + 1) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (X + 1) equal to 4.242640687 and -4.242640687.Subproblem 1
X + 1 = 4.242640687 Simplifying X + 1 = 4.242640687 Reorder the terms: 1 + X = 4.242640687 Solving 1 + X = 4.242640687 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 = 4.242640687 + -1 Combine like terms: 1 + -1 = 0 0 + X = 4.242640687 + -1 X = 4.242640687 + -1 Combine like terms: 4.242640687 + -1 = 3.242640687 X = 3.242640687 Simplifying X = 3.242640687Subproblem 2
X + 1 = -4.242640687 Simplifying X + 1 = -4.242640687 Reorder the terms: 1 + X = -4.242640687 Solving 1 + X = -4.242640687 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 = -4.242640687 + -1 Combine like terms: 1 + -1 = 0 0 + X = -4.242640687 + -1 X = -4.242640687 + -1 Combine like terms: -4.242640687 + -1 = -5.242640687 X = -5.242640687 Simplifying X = -5.242640687Solution
The solution to the problem is based on the solutions from the subproblems. X = {3.242640687, -5.242640687}
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