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Simplifying x + x(x + 1) = 17 Reorder the terms: x + x(1 + x) = 17 x + (1 * x + x * x) = 17 x + (1x + x2) = 17 Combine like terms: x + 1x = 2x 2x + x2 = 17 Solving 2x + x2 = 17 Solving for variable 'x'. Reorder the terms: -17 + 2x + x2 = 17 + -17 Combine like terms: 17 + -17 = 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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