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Simplifying (x + 6)(x + 8) = 5 Reorder the terms: (6 + x)(x + 8) = 5 Reorder the terms: (6 + x)(8 + x) = 5 Multiply (6 + x) * (8 + x) (6(8 + x) + x(8 + x)) = 5 ((8 * 6 + x * 6) + x(8 + x)) = 5 ((48 + 6x) + x(8 + x)) = 5 (48 + 6x + (8 * x + x * x)) = 5 (48 + 6x + (8x + x2)) = 5 Combine like terms: 6x + 8x = 14x (48 + 14x + x2) = 5 Solving 48 + 14x + x2 = 5 Solving for variable 'x'. Reorder the terms: 48 + -5 + 14x + x2 = 5 + -5 Combine like terms: 48 + -5 = 43 43 + 14x + x2 = 5 + -5 Combine like terms: 5 + -5 = 0 43 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-43' to each side of the equation. 43 + 14x + -43 + x2 = 0 + -43 Reorder the terms: 43 + -43 + 14x + x2 = 0 + -43 Combine like terms: 43 + -43 = 0 0 + 14x + x2 = 0 + -43 14x + x2 = 0 + -43 Combine like terms: 0 + -43 = -43 14x + x2 = -43 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = -43 + 49 Reorder the terms: 49 + 14x + x2 = -43 + 49 Combine like terms: -43 + 49 = 6 49 + 14x + x2 = 6 Factor a perfect square on the left side: (x + 7)(x + 7) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + 7) equal to 2.449489743 and -2.449489743.Subproblem 1
x + 7 = 2.449489743 Simplifying x + 7 = 2.449489743 Reorder the terms: 7 + x = 2.449489743 Solving 7 + x = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 2.449489743 + -7 Combine like terms: 7 + -7 = 0 0 + x = 2.449489743 + -7 x = 2.449489743 + -7 Combine like terms: 2.449489743 + -7 = -4.550510257 x = -4.550510257 Simplifying x = -4.550510257Subproblem 2
x + 7 = -2.449489743 Simplifying x + 7 = -2.449489743 Reorder the terms: 7 + x = -2.449489743 Solving 7 + x = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -2.449489743 + -7 Combine like terms: 7 + -7 = 0 0 + x = -2.449489743 + -7 x = -2.449489743 + -7 Combine like terms: -2.449489743 + -7 = -9.449489743 x = -9.449489743 Simplifying x = -9.449489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.550510257, -9.449489743}
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