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Simplifying (5 + x)(7 + x) = 72 Multiply (5 + x) * (7 + x) (5(7 + x) + x(7 + x)) = 72 ((7 * 5 + x * 5) + x(7 + x)) = 72 ((35 + 5x) + x(7 + x)) = 72 (35 + 5x + (7 * x + x * x)) = 72 (35 + 5x + (7x + x2)) = 72 Combine like terms: 5x + 7x = 12x (35 + 12x + x2) = 72 Solving 35 + 12x + x2 = 72 Solving for variable 'x'. Reorder the terms: 35 + -72 + 12x + x2 = 72 + -72 Combine like terms: 35 + -72 = -37 -37 + 12x + x2 = 72 + -72 Combine like terms: 72 + -72 = 0 -37 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + 12x + 37 + x2 = 0 + 37 Reorder the terms: -37 + 37 + 12x + x2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + 12x + x2 = 0 + 37 12x + x2 = 0 + 37 Combine like terms: 0 + 37 = 37 12x + x2 = 37 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 = 37 + 36 Reorder the terms: 36 + 12x + x2 = 37 + 36 Combine like terms: 37 + 36 = 73 36 + 12x + x2 = 73 Factor a perfect square on the left side: (x + 6)(x + 6) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (x + 6) equal to 8.544003745 and -8.544003745.Subproblem 1
x + 6 = 8.544003745 Simplifying x + 6 = 8.544003745 Reorder the terms: 6 + x = 8.544003745 Solving 6 + x = 8.544003745 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 = 8.544003745 + -6 Combine like terms: 6 + -6 = 0 0 + x = 8.544003745 + -6 x = 8.544003745 + -6 Combine like terms: 8.544003745 + -6 = 2.544003745 x = 2.544003745 Simplifying x = 2.544003745Subproblem 2
x + 6 = -8.544003745 Simplifying x + 6 = -8.544003745 Reorder the terms: 6 + x = -8.544003745 Solving 6 + x = -8.544003745 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 = -8.544003745 + -6 Combine like terms: 6 + -6 = 0 0 + x = -8.544003745 + -6 x = -8.544003745 + -6 Combine like terms: -8.544003745 + -6 = -14.544003745 x = -14.544003745 Simplifying x = -14.544003745Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.544003745, -14.544003745}
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