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Simplifying x(x + 7) = 73 Reorder the terms: x(7 + x) = 73 (7 * x + x * x) = 73 (7x + x2) = 73 Solving 7x + x2 = 73 Solving for variable 'x'. Reorder the terms: -73 + 7x + x2 = 73 + -73 Combine like terms: 73 + -73 = 0 -73 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '73' to each side of the equation. -73 + 7x + 73 + x2 = 0 + 73 Reorder the terms: -73 + 73 + 7x + x2 = 0 + 73 Combine like terms: -73 + 73 = 0 0 + 7x + x2 = 0 + 73 7x + x2 = 0 + 73 Combine like terms: 0 + 73 = 73 7x + x2 = 73 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 73 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 73 + 12.25 Combine like terms: 73 + 12.25 = 85.25 12.25 + 7x + x2 = 85.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 85.25 Calculate the square root of the right side: 9.233092656 Break this problem into two subproblems by setting (x + 3.5) equal to 9.233092656 and -9.233092656.Subproblem 1
x + 3.5 = 9.233092656 Simplifying x + 3.5 = 9.233092656 Reorder the terms: 3.5 + x = 9.233092656 Solving 3.5 + x = 9.233092656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 9.233092656 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 9.233092656 + -3.5 x = 9.233092656 + -3.5 Combine like terms: 9.233092656 + -3.5 = 5.733092656 x = 5.733092656 Simplifying x = 5.733092656Subproblem 2
x + 3.5 = -9.233092656 Simplifying x + 3.5 = -9.233092656 Reorder the terms: 3.5 + x = -9.233092656 Solving 3.5 + x = -9.233092656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -9.233092656 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -9.233092656 + -3.5 x = -9.233092656 + -3.5 Combine like terms: -9.233092656 + -3.5 = -12.733092656 x = -12.733092656 Simplifying x = -12.733092656Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.733092656, -12.733092656}
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