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Simplifying (x + 2)(x + 10) = 13 Reorder the terms: (2 + x)(x + 10) = 13 Reorder the terms: (2 + x)(10 + x) = 13 Multiply (2 + x) * (10 + x) (2(10 + x) + x(10 + x)) = 13 ((10 * 2 + x * 2) + x(10 + x)) = 13 ((20 + 2x) + x(10 + x)) = 13 (20 + 2x + (10 * x + x * x)) = 13 (20 + 2x + (10x + x2)) = 13 Combine like terms: 2x + 10x = 12x (20 + 12x + x2) = 13 Solving 20 + 12x + x2 = 13 Solving for variable 'x'. Reorder the terms: 20 + -13 + 12x + x2 = 13 + -13 Combine like terms: 20 + -13 = 7 7 + 12x + x2 = 13 + -13 Combine like terms: 13 + -13 = 0 7 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 12x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 12x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 12x + x2 = 0 + -7 12x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 12x + x2 = -7 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = -7 + 36 Reorder the terms: 36 + 12x + x2 = -7 + 36 Combine like terms: -7 + 36 = 29 36 + 12x + x2 = 29 Factor a perfect square on the left side: (x + 6)(x + 6) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (x + 6) equal to 5.385164807 and -5.385164807.Subproblem 1
x + 6 = 5.385164807 Simplifying x + 6 = 5.385164807 Reorder the terms: 6 + x = 5.385164807 Solving 6 + x = 5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 5.385164807 + -6 Combine like terms: 6 + -6 = 0 0 + x = 5.385164807 + -6 x = 5.385164807 + -6 Combine like terms: 5.385164807 + -6 = -0.614835193 x = -0.614835193 Simplifying x = -0.614835193Subproblem 2
x + 6 = -5.385164807 Simplifying x + 6 = -5.385164807 Reorder the terms: 6 + x = -5.385164807 Solving 6 + x = -5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -5.385164807 + -6 Combine like terms: 6 + -6 = 0 0 + x = -5.385164807 + -6 x = -5.385164807 + -6 Combine like terms: -5.385164807 + -6 = -11.385164807 x = -11.385164807 Simplifying x = -11.385164807Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.614835193, -11.385164807}
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