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Simplifying x(x + 1) + (x + 2) = 36 Reorder the terms: x(1 + x) + (x + 2) = 36 (1 * x + x * x) + (x + 2) = 36 (1x + x2) + (x + 2) = 36 Reorder the terms: 1x + x2 + (2 + x) = 36 Remove parenthesis around (2 + x) 1x + x2 + 2 + x = 36 Reorder the terms: 2 + 1x + x + x2 = 36 Combine like terms: 1x + x = 2x 2 + 2x + x2 = 36 Solving 2 + 2x + x2 = 36 Solving for variable 'x'. Reorder the terms: 2 + -36 + 2x + x2 = 36 + -36 Combine like terms: 2 + -36 = -34 -34 + 2x + x2 = 36 + -36 Combine like terms: 36 + -36 = 0 -34 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '34' to each side of the equation. -34 + 2x + 34 + x2 = 0 + 34 Reorder the terms: -34 + 34 + 2x + x2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + 2x + x2 = 0 + 34 2x + x2 = 0 + 34 Combine like terms: 0 + 34 = 34 2x + x2 = 34 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 = 34 + 1 Reorder the terms: 1 + 2x + x2 = 34 + 1 Combine like terms: 34 + 1 = 35 1 + 2x + x2 = 35 Factor a perfect square on the left side: (x + 1)(x + 1) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (x + 1) equal to 5.916079783 and -5.916079783.Subproblem 1
x + 1 = 5.916079783 Simplifying x + 1 = 5.916079783 Reorder the terms: 1 + x = 5.916079783 Solving 1 + x = 5.916079783 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 = 5.916079783 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5.916079783 + -1 x = 5.916079783 + -1 Combine like terms: 5.916079783 + -1 = 4.916079783 x = 4.916079783 Simplifying x = 4.916079783Subproblem 2
x + 1 = -5.916079783 Simplifying x + 1 = -5.916079783 Reorder the terms: 1 + x = -5.916079783 Solving 1 + x = -5.916079783 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 = -5.916079783 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5.916079783 + -1 x = -5.916079783 + -1 Combine like terms: -5.916079783 + -1 = -6.916079783 x = -6.916079783 Simplifying x = -6.916079783Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.916079783, -6.916079783}
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