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Simplifying (x + 13)(x + 7) = -3 Reorder the terms: (13 + x)(x + 7) = -3 Reorder the terms: (13 + x)(7 + x) = -3 Multiply (13 + x) * (7 + x) (13(7 + x) + x(7 + x)) = -3 ((7 * 13 + x * 13) + x(7 + x)) = -3 ((91 + 13x) + x(7 + x)) = -3 (91 + 13x + (7 * x + x * x)) = -3 (91 + 13x + (7x + x2)) = -3 Combine like terms: 13x + 7x = 20x (91 + 20x + x2) = -3 Solving 91 + 20x + x2 = -3 Solving for variable 'x'. Reorder the terms: 91 + 3 + 20x + x2 = -3 + 3 Combine like terms: 91 + 3 = 94 94 + 20x + x2 = -3 + 3 Combine like terms: -3 + 3 = 0 94 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-94' to each side of the equation. 94 + 20x + -94 + x2 = 0 + -94 Reorder the terms: 94 + -94 + 20x + x2 = 0 + -94 Combine like terms: 94 + -94 = 0 0 + 20x + x2 = 0 + -94 20x + x2 = 0 + -94 Combine like terms: 0 + -94 = -94 20x + x2 = -94 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = -94 + 100 Reorder the terms: 100 + 20x + x2 = -94 + 100 Combine like terms: -94 + 100 = 6 100 + 20x + x2 = 6 Factor a perfect square on the left side: (x + 10)(x + 10) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + 10) equal to 2.449489743 and -2.449489743.Subproblem 1
x + 10 = 2.449489743 Simplifying x + 10 = 2.449489743 Reorder the terms: 10 + x = 2.449489743 Solving 10 + x = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 2.449489743 + -10 Combine like terms: 10 + -10 = 0 0 + x = 2.449489743 + -10 x = 2.449489743 + -10 Combine like terms: 2.449489743 + -10 = -7.550510257 x = -7.550510257 Simplifying x = -7.550510257Subproblem 2
x + 10 = -2.449489743 Simplifying x + 10 = -2.449489743 Reorder the terms: 10 + x = -2.449489743 Solving 10 + x = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -2.449489743 + -10 Combine like terms: 10 + -10 = 0 0 + x = -2.449489743 + -10 x = -2.449489743 + -10 Combine like terms: -2.449489743 + -10 = -12.449489743 x = -12.449489743 Simplifying x = -12.449489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {-7.550510257, -12.449489743}
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