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Simplifying (x + 3)(x + 7) + -1(5)(3) = 1 Reorder the terms: (3 + x)(x + 7) + -1(5)(3) = 1 Reorder the terms: (3 + x)(7 + x) + -1(5)(3) = 1 Multiply (3 + x) * (7 + x) (3(7 + x) + x(7 + x)) + -1(5)(3) = 1 ((7 * 3 + x * 3) + x(7 + x)) + -1(5)(3) = 1 ((21 + 3x) + x(7 + x)) + -1(5)(3) = 1 (21 + 3x + (7 * x + x * x)) + -1(5)(3) = 1 (21 + 3x + (7x + x2)) + -1(5)(3) = 1 Combine like terms: 3x + 7x = 10x (21 + 10x + x2) + -1(5)(3) = 1 Multiply -1 * 5 21 + 10x + x2 + -5 * 3 = 1 Multiply -5 * 3 21 + 10x + x2 + -15 = 1 Reorder the terms: 21 + -15 + 10x + x2 = 1 Combine like terms: 21 + -15 = 6 6 + 10x + x2 = 1 Solving 6 + 10x + x2 = 1 Solving for variable 'x'. Reorder the terms: 6 + -1 + 10x + x2 = 1 + -1 Combine like terms: 6 + -1 = 5 5 + 10x + x2 = 1 + -1 Combine like terms: 1 + -1 = 0 5 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 10x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 10x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 10x + x2 = 0 + -5 10x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 10x + x2 = -5 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -5 + 25 Reorder the terms: 25 + 10x + x2 = -5 + 25 Combine like terms: -5 + 25 = 20 25 + 10x + x2 = 20 Factor a perfect square on the left side: (x + 5)(x + 5) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x + 5) equal to 4.472135955 and -4.472135955.Subproblem 1
x + 5 = 4.472135955 Simplifying x + 5 = 4.472135955 Reorder the terms: 5 + x = 4.472135955 Solving 5 + x = 4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 4.472135955 + -5 Combine like terms: 5 + -5 = 0 0 + x = 4.472135955 + -5 x = 4.472135955 + -5 Combine like terms: 4.472135955 + -5 = -0.527864045 x = -0.527864045 Simplifying x = -0.527864045Subproblem 2
x + 5 = -4.472135955 Simplifying x + 5 = -4.472135955 Reorder the terms: 5 + x = -4.472135955 Solving 5 + x = -4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -4.472135955 + -5 Combine like terms: 5 + -5 = 0 0 + x = -4.472135955 + -5 x = -4.472135955 + -5 Combine like terms: -4.472135955 + -5 = -9.472135955 x = -9.472135955 Simplifying x = -9.472135955Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.527864045, -9.472135955}
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