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Simplifying (x + 1)(x + 3) = 72x Reorder the terms: (1 + x)(x + 3) = 72x Reorder the terms: (1 + x)(3 + x) = 72x Multiply (1 + x) * (3 + x) (1(3 + x) + x(3 + x)) = 72x ((3 * 1 + x * 1) + x(3 + x)) = 72x ((3 + 1x) + x(3 + x)) = 72x (3 + 1x + (3 * x + x * x)) = 72x (3 + 1x + (3x + x2)) = 72x Combine like terms: 1x + 3x = 4x (3 + 4x + x2) = 72x Solving 3 + 4x + x2 = 72x Solving for variable 'x'. Reorder the terms: 3 + 4x + -72x + x2 = 72x + -72x Combine like terms: 4x + -72x = -68x 3 + -68x + x2 = 72x + -72x Combine like terms: 72x + -72x = 0 3 + -68x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -68x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -68x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -68x + x2 = 0 + -3 -68x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -68x + x2 = -3 The x term is -68x. Take half its coefficient (-34). Square it (1156) and add it to both sides. Add '1156' to each side of the equation. -68x + 1156 + x2 = -3 + 1156 Reorder the terms: 1156 + -68x + x2 = -3 + 1156 Combine like terms: -3 + 1156 = 1153 1156 + -68x + x2 = 1153 Factor a perfect square on the left side: (x + -34)(x + -34) = 1153 Calculate the square root of the right side: 33.955853693 Break this problem into two subproblems by setting (x + -34) equal to 33.955853693 and -33.955853693.Subproblem 1
x + -34 = 33.955853693 Simplifying x + -34 = 33.955853693 Reorder the terms: -34 + x = 33.955853693 Solving -34 + x = 33.955853693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '34' to each side of the equation. -34 + 34 + x = 33.955853693 + 34 Combine like terms: -34 + 34 = 0 0 + x = 33.955853693 + 34 x = 33.955853693 + 34 Combine like terms: 33.955853693 + 34 = 67.955853693 x = 67.955853693 Simplifying x = 67.955853693Subproblem 2
x + -34 = -33.955853693 Simplifying x + -34 = -33.955853693 Reorder the terms: -34 + x = -33.955853693 Solving -34 + x = -33.955853693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '34' to each side of the equation. -34 + 34 + x = -33.955853693 + 34 Combine like terms: -34 + 34 = 0 0 + x = -33.955853693 + 34 x = -33.955853693 + 34 Combine like terms: -33.955853693 + 34 = 0.044146307 x = 0.044146307 Simplifying x = 0.044146307Solution
The solution to the problem is based on the solutions from the subproblems. x = {67.955853693, 0.044146307}
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